Hi Brian
I do sympathise with you as I have the same problem, and also tried various combinations of bedding. The original caravan cushion was too firm for me so we had it refoamed, which although better, is still too firm. I should have gone for a softer foam, although at the time, I was worried about it being too soft when used as a seat. A 2" memory foam topper was next which did make the bed much more comfortable, but did also prove to be a little hot. I now sleep on top of a cotton sleeping bag with a duvet on top and this is less hot, but not as soft!
However, I have now discovered a new memory foam called polar foam, by QVC and I have just last night, ordered a topper for the bed at home. This is marketed as being much cooler than original memory foam. We are going away on Thursday until Tuesday so hopefully it should be here on our return. I will let you know the outcome.
In your case, I agree with Lutz, remove the airbed, as these cannot breathe at all. Use as much cotton as you can, sheets, covers, pyjamas etc., whichever you use as polycotton, especially underneath cannot breathe at all. If I find a definite solution I might market the idea!!