Cool. your sig says 2010 so I thought it was Gen3 but just wanted to be sure. The Gen2 prius doesn't have the EV button as standard equipment in the US, but it does in some other countries, including Australia. Anyway I get exactly the same issue with my Gen2 and the EV button. It just stops working when the temperature is too hot. I think the EV button is considered as a very non-essential feature and shuts of even at fairly mild battery temperatures. Note that EV mode still works even when the EV button is disabled, as in the car will still drive under purely electric power at low speed or low power requirements as per usual. If however the battery really gets too really then the computer will just about completely inhibit running full EV operation at all, and the engine will run all the time. Hopefully you rarely or never get that condition.
I'd be curious to see the difference between leaving your windows down and having the AC set 2 degrees below the outside temperature. I'm often caught driving with my windows for two reasons: 1. The tint is illegal 2. I like to share my music with the world. If/when I do roll my windows up, I'll usually set the temperature 2 degrees below outside temperature. I don't have a scangauge nor the patience to test it, but I'd still be curious to see the results.
LOL for us that is considered a foothill. I don't like to run the AC so I usually just crack the driver's side window and the rear passenger window. This circulates the air quite well and there is no need to mess with the fan settings. In extreme heat (100+) then the AC is the only thing that works. I don't mind losing 1-2mpg to run it at those times.