A little more info for using a heated mattress pad on an air mattress. We have always put a standard cotton mattress pad on top of the air mattress and under the heated mattress pad and is probably why the AeroBed, Coleman, and Intek air mattresses have lasted so many years without developing leaks. 22 years and still no leaks in the TC's. I feel that putting the HOT heated mattress pad directly on top of the vinyl plastic mattress would shorten it's life or cause leaking far more quickly.
All our RV's we've had since 1983 have had an inverter used in them starting with our first inverter owned which was an 1800 watt Heart Interface. The Heart Interface was actually purchased for use in our 30' Catalina sailboat and then the 34' Catalina but was very easy to disconnect and also use it in our RV's for 110 AC when off shorepower. It was heavy unlike the inverters of today but sure did work great as long as you had several deep cycle batteries. Had a built in 65 amp charger to recharge the batteries when the engine is running. Our AeroBed pump runs on 110AC and so does our heated mattress pads and having an inverter solves that when being off the grid.
Sure wish AeroBed still made the 8" thick model with the dual sides inflation control internal pump and a wired remote pod as I'd buy another one for the 5th wheel in a heartbeat. I'm limited to 8" thick in the Lance TC cabover bed as if any thicker it would block the wardrobe cabinet door from opening. Even a 10" would work fine in the 5th wheel as nothing is in the way but we'd probably have to leave the 2" thick memory foam off that is on the present 8" Intek as it makes it too high to sit on the edge of the bed. Maybe we both just need 2" longer legs!!!