Thanks for your replies. Yes, I will have to use NiMh batteries, no problem. For the temperature, i would probably use a PID and a temperature sensor.
But I think it wont work to heat an LCD from behind. The heat wont arrive on the front side without heating extremely. To make it a bit clearer, I am a Hot Air Balloon pilot, and we do have instruments with huge LCDs (although black and white and without touchscreen, but they are 15x8cm) which work under these conditions. Since it is an device for flight safety I wont open it to look how they're doing it.
Do there exist like LCDs that are made for these conditions? Any other solutions?