The Prius' primary goal is to produce minimal emissions. To do this it must keep the cat and engine warm. My observations so far indicate my car (Pearl) thinks 60C and above is warm (coolant temp). So whenever you start cold, the car will warm up the engine and cat by not shutting the ICE off until it starts to warm up.

When you stop somewhere, do something for a few minutes, then get back in and restart the vehicle, it will again run the ICE for a minute or two, probably to warm up the cat (I can only monitor the ICE temp., not the cat temp, and the ICE was still fairly warm), but it will shut down much quicker than if it was cold.

As far as battery operation in extreme temps (90F and above), the system will try to protect the battery. It uses cabin air to cool the battery, so use your A/C to give it cool air. NiMH batteries have a negative temperature vs voltage response, so a hotter battery will have a lower voltage. Combine this with the higher voltage at higher charge, throw in the possibility of incomplete compensation, and you can see how the SOC meter could be confused. It's probable the system is more careful with the battery when it's hot. Not charging it as much and not using it as much. This is because using or charging it will result in more heat.

Pearl is a
2007 Driftwood Pearl Prius
Package "B" (everything but leather, nav, and rear camera)