I have a 2002 and I live in Wisconsin. Every summer, I am intrigued how the AC system (belt driven off the engine) can keep cold air blowing without the engine on.
It definitely depends on the ambient temperature, but in the right conditions I can sit for a minute or so without running the engine. The air will slowly warm up after that initial minute, and the engine will light (usually ~10-15 seconds after the air STARTS getting warmer) to run the compressor. After about 15-20 seconds of engine run, the air is ice-cold. The engine quits, and the air stays cold!
Obviously, the initial cooling requires the engine to run most of the time, but once the cabin is mostly down to my typical setpoint of 75, I can stop at a light or sit in traffic without losing cold air for a solid MINUTE. I did a worst-case-scenario test with auto climate set to 70 at 95 degrees ambient, and I was still able to get 25-30 seconds of ice-cold air without the engine. Engine runtime in that case was still around 15-20 seconds, maybe 25.
I tested several conventional vehicles to see if this was just a given with AC evaporators. Tried to mimic the same engine run-stop patterns as my Classic in a Dodge, a Chrysler minivan, and a Honda, and I could only get 10-15 seconds of cold air. The air QUICKLY warmed up.
The only (fairly) conventional vehicle that could maintain cooling with the engine off was my grandpa's Acura. That car has idle-start-stop and apparently a special "cold storage" evaporator that is able to freeze a (thermally massive) solution in its core so it can stay colder for longer. Is there similar tech. in my Prius? Or is it just that Toyota oversized the evaporator, and therefore it has more thermal mass?