Whoa! I never meant to imply that a thicker base would spread the heat quicker! The purpose of a thicker base is to spread the heat, so that the deltaT is at a point where the water can pick it up better.
Think about an extreme: if the source heat was say 300 degC (assume a 1500W source), the water would pick up a lot of energy, but it certainly wouldn't pick it up fast enough to lower the temp back down anywhere near 20 or 30 deg C.
I think that's where your thinking is at. Yes, a higher temp will transfer more heat, but you're also allowing your source to remain hot.
There is an optimal set of conditions at which the water will transfer the most amount of heat, a.k.a. a maximum efficiency point. You're just shooting for maximum heat, without considering the efficiency of the heat transfer. That's what's biting you in the rear end!
