Nice Avatar, OP!
I think another reason so many men were wearing suits at baseball games, etc. is that people didn’t have walk-in closets full of clothing like we do today. They had clothing that they worked in and clothing that they went to church and funerals in. A man would not go to an outing in his overalls, he’d wear his “good” clothes.
Yes. In the days when 90% of the population did hard physical labor, the suit and tie was an escape from the weekday drudgery.
I just got really hot. I used to have to wear suits going to work every day, and NYC summers can get warm. The office was obviously air conditioned, but back in the 80s, lots of the subways weren’t, and the walk from the subway to the office wasn’t, either. Standing on the subway, pressed in between people and feeling the sweat roll down your back – good times. At least with three layers (undershirt, shirt, jacket), you were pretty sure that sweat was yours.
Sweat stains used to be a lot more prevalent. I’m surprised when I see 60s or 70s tv shows where the actors are visibly sweating with huge pit or back sweat (and it isn’t important to the plot, it just is there.)
Gosh, you have taken me back to going to church as a kid. On hot Sundays virtually all of the ladies and a fair number of men would be constantly fanning themselves with those folding hand fans, which you could also make for yourself by accordian-folding the church bulletin. Bet the kids at the hip megachurches these days don’t put up with that s**t. 
As I observe in the companion thread to this one, John Gorrie in Appalachicola Florida invented a refrigerator to bring comfort (and, he hoped, a cure) to his Yellow Fever victims in 1844 and was granted a patent in 1851. This was a practical air conditioning device, which he used to cool hospital rooms. He could also use it to make ice. So “air conditioning” was invented well before 1901. In fact, Gorrie was by no means the first to invent an air conditioner.
“Dr. John Gorrie Marker, Apalachicola, FL” by George Lansing Taylor Jr..
https://www.phys.ufl.edu/~ihas/gorrie/fridge.htm
However, your point about air conditioners not being in wide use until the 1950s is correct. I haven’t looked into why. But I recommend you read Alistair Cooke’s essay “The Summer Bachelor” about the social effects of no air conditioners. You can’t understand the movie the Seven Year Itch without this information.
Back in the early 2000s, a college friend was ordained as a Universalist minister, in a tiny town in northeastern Georgia. The congregation was around seven elderly people, and the ceremony was held in their 19th c. white clapboard church. No air conditioning, so they opened up the tall, gothic-arched casement windows. The pews were liberally scattered with paper fans that - of course - advertised the local funeral home. The town was so small that the funeral home’s phone number was only four digits.
I felt like I had stepped into a Harper Lee novel.
At least, suit-wearing fans at old-time baseball games didn’t have to exert themselves.
Players wore wool flannel and long sleeves into the 1940s.
Even elegantly dressed manager Connie Mack evidently took his suit coat off in the dugout in the hottest weather (he may be fanning himself with the lineup card in the linked photo).
Whenever I see those photos of people in the stands wearing suits I wonder about a few things. One of the things I wonder about iswhether tickets were almost always so expensive that only fairly wealthy people could attend. Another thing is that the photos always seem to be near the field - how were the people in the bleachers dressed ? Also, people would generally be going straight to the game from work on a weekday. I always kind of wonder how much of “people used to wear suits to baseball games” is really " the relatively wealthy people in field level seats who came to the game straight from work wore suits". Because one thing I’m certain of is that the men in my family didn’t wear suits “all the time” - wedding, funerals and maybe church, but not all the time. Not to work - they didn’t have jobs that were conducive to suit wearing. And not around the house. I’d be really surprised if they wore their one suit to a baseball game . Now, they weren’t wearing jeans or overalls and t-shirts either, so they probably would still look “dressed up” to later generations.
He may also be signalling. He used the lineup card to tell his players where he wanted them. The rules of baseball said that only uniformed people were permitted on the field - it’s why managers still wear a uniform - and as he refused to do so, he could only signal from the dugout.
Short sleeve oxfords and ties were pretty standard middle class workwear in the 1960s. Men teachers wore that in un-AC classrooms. NASA Mission Control was a sea of guys dressed like that. My dad was a draftsman for a microswitch supplier to the space program, and it was his uniform.
Nah, tickets weren’t always so expensive. Certainly not Yankees or Dodgers expensive. Tickets to sporting events at the low end (small market teams with poor records) are similar to what they were but the ones at the high end are ridiculous now.
A lot of people in the stands really were wearing suits. Maybe not everybody, but those who weren’t were certainly wearing “appropriate” clothing which would often include a jacket of some sort. So that part tracks. They would be dressed much more warmly than we do now, where even in air-conditioned indoor stadiums people may wear t-shirts and short pants.
This was my home town until more recently. There was a 3 digit prefix but since it was the same for everybody, you went around only telling people 4 digits. Apparently they recently got a second telephone prefix. I probably still remember a dozen of those 4 digit phone numbers.
Yes, I know (it’s a joke, son).
In Ty Cobb’s “authorized” autobiography, he talks about playing for the Athletics in his final seasons and Mack signaling him where to play various hitters (supposedly Mack was never wrong in this regard).
The current heat injury training we get yearly states that it takes two weeks for a worker to acclimatize to the heat, and that therefore new workers need to take water/shade breaks more often.
Anecdote: I used to know a guy who worked Renfairs. He said it was easy to deal with the heat once he acclimated, but drinking iced drinks or walking into AC would break the acclimation. It wouldn’t break it completely, but he’d be uncomfortable until he re-acclimated.
Acclimatization will help you function to an extent but you won’t be comfortable. It’s just something they dealt with and sweated through.
And it’s hardly new. Though the extent is greater, every summer people in northern cities do die of heat because there’s less A/C up there. In the worst summers, this would be hundreds of people, usually the most vulnerable (the elderly, the young, or the sick). And that’s in an industrialized country like the US and has been happening for decades.
And there were reports of dozens of people recently dying on the Hajj in 120 degree heat. Those aren’t all people who would be used to A/C, either.
There’s only so much our bodies can do to adapt to high heat.
It is hard to compare prices with today’s, but I can tell you the price of tickets at Shibe Park, later Connie Mack stadium, in the early 50s. Bleachers, $.50, general admission $1.30, Reserved seats (basically seats in the lower deck in the first 7 rows–i.e. in front of the pillars) $2.00 and box seats (field level) $2.50. We were very lower middle class, but $1.30 was no prohibitive. Later in the decade, they started moving the boundary between general admission and reserved seating until there was no more general admission.
To get back to OP, I never understood how people put up with the summer heat either. In Philly, temperatures in the 90s were no uncommon (although I don’t recall it ever hitting 100) and indeed many men wore woolen suits every day. By 1950 you could get short sleeve dress shirts, but that didn’t help much. And the baseball players wore woolen uniforms. At least they spent half the game sitting in the dugout, but the poor umpires spent the whole game in their black woolen suits under the hot sun. I don’t know how they did it.
Lightweight wool is cooler than you think. Smartwool and others make merino wool underwear, Tshirts etc, and they are cooler than cotton, as they breathe better. Tropical weight wool is pretty lightweight , and then a Panama straw hat- really pretty cool.
Wool can be thick and hot or thin and cool.
One thing I would like to add. The first public businesses to air condition were movie houses. At least in Philly, they used to close during July and August because few would come in to the closed environment. After AC not only did they get business during the summer, but people would go as much for two hours of cooling off as for the movie. Maybe more.
I grew up in New England without air conditioning, and i hated the heat. I remember whining to my parents about not being able to sleep because it was too hot.