There is quite a bit of ventilation under there. It's open on the top and one side, so I think pretty much free flowing - certainly compared to a cabinet. I don't have a pic handy of mine, but it's in a space something like this:
http://www.rvdap.com/image/ilmx/2011-pleasure-way-excel-ts-jsmmlv.jpg.
It's certainly won't be in direct contact with the bed, and will be installed with the required clearance on all sides. Outside of a serious malfunction, it will never reach any kind of temperature that would start a fire. If there is a serious malfunction, well then all bets are off.
Personally I don't have a generator - solar only - and am boon-docking close 100% of the time, so an inverter is a must. About the size - most of my demands are small, but the microwave is 1000W, the space heater is 750W to 1500W and SO has a hair dryer at around 1500W. The price difference and efficiency gap isn't large, so I just got a unit big enough to run everything. It only added a couple of pounds.
