Paula, I am surprised the thermostat fixed you car, it sounds like a classic fan clutch or clutch circuit issue. It could have been a thermostat switch for the fan maybe?
Yes, thermostat switch for the fan. The fan wasn’t coming on, thus the overheating while sitting still but not while driving. The mechanic knew what I meant when I said “I think the thermostat thingie is broken.” 
I had an electric radiator fan fail because the fuse blew. I didn’t have time to pull over and diagnose the reason the fan stopped working-- all I knew was that every time I stopped at a light, the temperature gauge crept up near the red. So I turned on the heater and rolled down all the wondows. Then when I was moving, I turned it off, and from driving, there was air moving through the radiator, and the gauge needle went down, so clearly there was fluid and it was circulating.
I had a baby at the time, so I went home, parked the car and waited for DH to come home. Then I went out and looked at the car. By then it was cool, so I verified that it had enough coolant, and that the radiator thermostat seemed to be working (I took it out and put it in boiling water, and it opened; I put it back).
I pulled the fan fuse, and it had blown. I replaced it, started the car, and drove it around close to the house until I got it up to temperature, then drove it home and popped the hood. The fan was on, and it stayed on. The temperature gauge needle stayed where it should, just a little under the halfway mark.
I never pinned down just why the fuse had blown, but I had a pretty good idea. It never blew again. This was about six years ago, and the same fuse I replaced is still working.
Anyway, this is when turning on the heater works: when the engine stays cool while you are moving, but starts to overheat at a standstill. This means that your radiator fan isn’t working, but you can use the fans the blow on the heater core instead, when the car is stopped, and otherwise depend on airflow over the radiator from the car moving.
If the engine is overheating while you are moving, something else is wrong: your coolant has leaked out, or your thermostat is plugged, so the coolant can’t circulate. You need to pull over STAT, or your engine is junk.
Or it’s a 2-speed Hondamatic Wagon trying to make it between San Jose and Santa Cruz. 
That tough little car made that trip dozens of times without failing. It just needed that little help on the uphills. Turning on the heater would drop the gauge from just below red to about 3/4.
The ol’ heater trick worked best on cars that had a valve that controlled coolant flow to the heater core. More commonly on newer cars, coolant circulates through the core all the time and the temp control only affects the amount of air that passes through the core on its way to the vents. Upping the amount of air going through the core helps a bit, but since there’s always a certain amount of heat being carried away by the core even with the heater off it’s less dramatic.
I used to have a recurring problem with my radiator leaking, and discovered the trick on my own. It’s not a substitute for a radiator, but it has saved my ass and gotten me home on many an occasion (Honda Civic 98).