The decision on how to power your trailer really depends on your planned locations. Will you have shore power? Is there a limit on your power usage? If you are doing festivals and have shore power, make sure what is available. Around here they almost all have some power, but usage and type is limited. There are very few places with 220/240V.
If you are going to be mobile and self powered, I would go with as much propane as possible. For anything electric, check wattage and go with the most efficient available. A small appliance that uses half the wattage may cost more up front, but in the long run you'll save on fuel costs. When calculating energy usage for your generator requirements don't forget to take everything into consideration; lights, exhaust fan, water pump, etc. and leave a little room in case you need to add something later.
Can't really answer regarding heat affecting appliances - It's almost never that warm here. :)
post edited by Noodles on the Loose - 2013/03/04 13:26:41