Hi we3pete,
Most pocket coil innersprings or other types of innerspring that have been specially constructed to work with an adjustable bed as well as most “all foam” mattresses will work fine on an adjustable bed. It’s always best to check with the manufacturer though to make sure that using the mattress on the adjustable is covered by their warranty.
Innersprings are deeper support layers and they all have some type of comfort layers (usually some type of foam or fiber) over them which will either improve or detract from temperature regulation more than the innerspring itself. You can read more about the different factors that affect the sleeping temperature of a mattress in post #2 here and post #29 here. Out of the three main types of foam (polyfoam, memory foam, and latex) … latex is generally the most breathable and sleeps the coolest all other things being equal. The layers and components that are closer to your body will have a bigger effect on temperature than the deeper layers so if a mattress had an innerspring and then 4" of Talalay latex and another mattress had 6" of latex or polyfoam as the support layer instead of the innerspring and had the same 4" of Talalay latex on top and they all had the same types of cover and quilting and protector and sheets and bedding they would be roughly the same in terms of temperature regulation because the type of support layer in the mattress would have the least effect on temperature.
Phoenix