My coworker would like to know why I think a floor with a vinyl/plastic surface would heat a room more than a floor with a tiled surface? To me this makes common sense but he wants a more physics based answer because he has no common sense.

Well, if you have common sense and he doesn't, tell me why you " think a floor with a vinyl/plastic surface would heat a room more than a floor with a tiled surface."

Because if your reasoning is wrong, the answer will be obvious.  If you are correct, it will be equally obvious.