Quite a bit, actually. It's why high end telescope CCDs do similar things. A high ISO means you're ramping up the gain, so the bits of random noise get amplified too. Cooling it means you're getting rid of one of the more significant sources.

You'll notice on this page - http://www.primalucelab.com/astronomy/d5500a-cooled-camera.h... - that the before/after photo is taken at ISO 6400.I consider that to be reasonably high ISO. But yes, at some point, heat is not the primary issue anymore.

On a CMOS higher ISO is just increased analog amplification. If your pixel is measuring thermal noise the. You will amplify that too I guess.