If the floor under the accelerator is hot enough for the epoxy to break down, you'd know it from driving having very uncomfortable feet (at the least)!
What sort of "tile" is this? Is it vinyl or ceramic? If it's vinyl, I don't know whether or not epoxy would stick--though I suspect it would--but I do know that thin set or other cement-based mortar would not be a good choice.
If you do use epoxy and there are voids between the tile and the floor substrate, add some thickener to the epoxy like microbaloons or silica or possibly even sawdust. A store like West Marine would have these sorts of materials and possibly someone who could advise you on what would be reasonable to use. Epoxy by itself is rather brittle (and expensive).
If it were me, I don't think I'd care for tile in that area at all, for what it's worth. That's just my preference.