||Part of the reason more powerful cars run wider tires is because they have to dissipate more heat. Even when the tire is not (grossly) slipping, it is absorbing a percentage of that energy as heat in the process of transferring it to the ground. More energy=more heat.
What you said is true, friction coefficient is affected by temperature. That's why drag cars do a burnout, to get the tire up to temperature. The problem comes when you're putting more heat into the tire than it can shed, and the tire gets too hot and starts to get greasy. Too wide a tire though, and the tire won't ever get up to temp.
I'm currently playing this game with my Z. I'm currently running a 255/40/17 Federal 595RSR on all 4 for autocross. This is unfortunately the widest most 200 treadwear tires come for a 17" wheel. I've been running 17s because their tires are ~$90 cheaper than the 18" alternative. The problem is that I overheat my tires quickly and have to sit out for a while, or spray the tires down between runs.
I need to
A: Get a tire temp probe to check that I'm heating the tire evenly. I'm suspicious that I'm actually only overheating the outer shoulders and in need another degree or 2 of camber.
B: Possibly get more tire. Either a wider tire, but that'll mean going to <200tw R888 or NT01, which aren't cheap. Or switch to 18s where I can get a 275/35/18 and handle more heat.
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