@dan Y. No, in this scenario there is no heat rising up the side of the cup, just boiling water poured in - or else stove turned off by coffee still hot.
Even in the external heat scenario, which is not really the case I think we were referring to, it is the specific heat, not just the heat itself, which determines the heat transfer/comfort to your fingers. So for example, Styrofoam (assuming it would not melt already under those conditions) would feel less hot than metal at the same temperature (over the short term).
Another example is why you don't lick a metal bar when it is freezing outside. So it IS a legitimate question. Now who shall we get to test it out. "Hey mikey, go pick up that mug."