Technically all coolers work better on a hotter CPU. They are able to transfer more total energy with a higher temperature differential. (yes, that is a thermodynamic concept)
It's a bit more complicated than that... Only if you have enough differential at the "ends" and the metal is not saturated what you said is kind of true. At the end of the day, surface area is what you want when your transport is the same (as in, same metal composition). Also, the temperature differential the fan makes is non-trivial either. You can "force" a differential with a bigger fan up to a point.
Regardless, it doesn't make sense to me for the exact same cooler and fan to perform better on a CPU that produces more heat per area than another which doesn't. We're not talking about low power either. If it was, say 15W vs 25W, sure, the 25W will saturate the surface area of the heat spreader better and move more heat out, but we're talking about parts which are over 125W for a cooler that's, more or less, rated for 95W, so it'll be saturated from the get go.