I just posted,
elsewhere, about my preference for an air mattress, before I found this thread.
I will add, here, that I do not have any problems with the mattress feeling cold, because I use a 3" slab of memory foam on top. I also don't get sweaty because the memory foam is a special version that is breathable. Though I can't remember for certain, I am pretty sure
this is what I have. It did cost about $99 at Costco but it was worth it.
I solve the problem of the sheets coming off by using fitted sheets made for extra thick mattresses. They wrap around much further. You can also buy little straps, kinda like old nylon-hosiery straps, that will hold the sheets in place. Though I don't have a clue where to get them.
When I move to a van, I plan to sew a cover, more like a futon cover, for my mattress/foam combo so my bed can look more like a sofa when I am not sleeping on it.
Good, Coleman air mattresses can be pumped up pretty firm and do not squish out from under you at all, when you move around. I often have to stand on mine to get to boxes on a shelf over my bed. It is about the same as stepping on a regular bed.