I seem to remember that, when I was growing up, if you went to a restaurant you generally got your meal on a room-temperature plate, just like at home. Nowadays, it seems that whenever I eat out, I have to be extremely careful NOT TO TOUCH MY PLATE for fear of receiving third-degree burns. I can think of several potential rationales for this: (a) Reduces risk of contamination; (b) Maximizes piping hot goodness; © Is in some way cheaper for the restaurant. Does anyone have actual inside information on the reason for this trend?
B mostly, heat transfer from hot food to a cold(er) plate can cool down food very fast, which can hurt the customer’s perception. Easy enough to keep the plate hot so even huge portions don’t get cold by the end.
Probably also a little bit of lawyer-fear in there as well.
I can think of a couple other possibilities.
d) heat lamps - if your order is done before the rest of the parties, your food+ plate may spend time under a heat lamp. Heat lamps will heat up both the food and the plate
e) melted cheese - many times, when a server has to tell me “Don’t touch that plate, it’s really hot”, it’s because I’ve ordered something with melted cheese on top. The food is plated, the cheese added, and the whole thing is popped under a broiler in order to melt and brown the cheese. Heating up the plate is a side benefit.
Dishwasher temperature is a factor too. Plates come out of the dishwasher extremely hot, and during busy time are often run right back over to the plating area.
The only time I can recall being told this in recent memory is when I ordered a skillet meal. Since the skillet presumably comes straight off the oven and it’s cast iron, it’s going to retain heat really well.
I often see this in Italian places, where you might get a baked dish (usually with cheese on top), such as lasagna, ravioli, etc. The entree is usually baked in the serving dish, which is itself placed onto a room-temperature plate for easier handling. The server then cautions diners to not touch the upper dish, which is scalding because it spent an extended time in the oven/broiler, and had just been removed.
I also see this in Mexican restaurants, where many plates are briefly placed directly under the broiler to melt the cheese topping. The plate is hot, but nearly as hot as the baking dishes in Italian restaurants. In Mexican restaurants, the server either wears an oven mitt or has very tough hands. 
They simply say, “Hot plate!”
I think that the dishwasher and food lamp heat have also led to restaurants to want to serve all their plates hot, so that it’s seen as consistent and no one can tell that their food sat under the heat lamp while someone else’s well-done steak finished cooking or worries that their plate was run through the dishwasher too quickly and wasn’t sanitized or given time to dry.
No. I have the opposite observation. I was about 6 years old in 1974, when I was given a warm plate. I was confused, and a grown-up told me that was a sign of a classy restaurant doing things properly. My salad would arrive soon, and my plate and fork would be chilled. And they were. Remember, on the T.V. show MAS*H, Charles is stunned that the salad forks in the mess tent weren’t chilled. So yeah, it’s been a tradition in fine dining for a while.
This is also a reason. Dishes taken straight from a dishwasher to prove that they’re clean, or just by coincidence. Once I had sashimi on a piping hot plate. I’m not such a fussy gourmand that I would really complain, but it is a funny occurrence.
It is not done to improve the dining experience.
Sometimes plates are stacked on top or under of the heat lamps making them super hot. Largely due to convenience. If the top plates stacked under the lamps have not been used for a time they get screeming hot. If stacked on top the bottom one are skorchers. Sometimes they are stacked above the burners. Sometimes the food has been sitting under the heat lamp for to long. As mentioned before it may have been placed under a broiler or salamander for a bit. A warm plate is nice a hot plate is just the internal workings of the particular kitchen. Kitchens Are mighty hot places and many scenarios can contrbite to a very hot plate but there is no one in the back heating them up for your dining pleasure.
You should be able IMHO to touch your plate with out fear. And not be presented with danger
pre-cooked food that is microwaved as needed.
My grandmother has always heated up my grandfathers plate. It keeps his food warmer for longer.
Well, I like to have my hot food at home on a hot (not just warm) plate too.
MY thought.