I'm gonna go with "not much".
I found this article,
Reflection Measurements in IR Spectroscopy
And in it, I recognize many English words, but they did not seem to be arranged in a coherent fashion that I could well understand. Maybe you have more luck or skill than I. It seems written for an audience, a party to which I was not invited.
What I can distill from it is this:
Heat can be reflected (back), transmitted (through), or absorbed (kept, and not reflected or transmitted). I suspect that heat will be split all 3 ways (some being reflected, some being transmitted, and some being absorbed), and, the material which allows more heat to be reflected more than it is transmitted or absorbed will be more effective for this particular purpose.
The article also states that reflection takes place at the surface. My guess is, a foam padding painted with aluminum reflective paint or such coating will effectively reflect, but probably not with someone sleeping on it, which will disrupt the reflection. Because the surface is distorted when slept upon, the foam material is the next line of defense against transmittal of heat, and all we can do is hope for as much absorption as possible.
My guess, then, the thinner the foam, the less absorption and greater transmittal occurs, and that factor can be determined by the material's ability to compress, and, the weight of the person sleeping on it. A child, for example, might find it warmer than an adult might, because there is less deformity of the surface, and, when compressed, is less so than when an adult sleeps on it.