It's not always being cooler per se that makes the difference; other problems such as electron tunnelling (we're getting well beyond my paygrade, there's a lot

It's not always being cooler per se that makes the difference; other problems such as electron tunnelling (we're getting well beyond my paygrade, there's a lot more) can be limited with a better hardware design (say tapeout) as well. But yes, you get better performance from being able to function at a higher frequency on a large die (with more heat, but that wasn't necessarily the limiting factor previously) or on a smaller die where the parts are now closer together and so take less time and energy (heat) to communicate. A better tapeout geography can mean fewer lost cycles waiting for this or that info to get where it's going and so actually increase useful IPC at least a bit.