Air mattresses are cold. As a camp ranger for the scouts I saw countless examples of people unhappy with them. If used, they should be topped with a foam pad for body heat retention. Air wicks the heat away from your body. Any space larger than 1/4 inch will be subject to convection currents and heat loss/transfer. Trapping dead air in small spaces such as down, foam or hollow fibers that prevents these currents creates an insulated layer.
Air mattresses work well to transfer heat away from you when camping in hot weather but can be too cold in the morning. An air mattress seems to deflate because as the ambient air cools so does the mattress resulting in less pressure. Some just leak.
I use the memory foam topper on my factory mattress for a great night's sleep. It is hard as a rock when cold, so keep it warm if you plan on sleeping on it that night. An electric blanket or heated mattress pad would work well.