> I've been searching for a laptop that stays cool, even when pushed
That would be an intentionally throttled laptop, which is not what most people would want. Because if the laptop "stays cool even when pushed", it means it could have been pushed more.
However, if low thermal output is what you want to optimise for, then an M1 macbook air always running on low power mode is a very good candidate, and abundant in second hand market for very good prices. Or any M1/M2/M3 laptop as long as you run it on low power mode.