Overheating is a bit of a misnomer; the Exynos models have quite restrictive thermal throttling because it can't keep up under sustained load, which is going to be typically gaming. Even the Snapdragon one's will thermal throttle eventually under load, they just have better thermal management so they can sustain performance for longer. It is highly unlikely you will encounter this under light usage. 

In saying that, it would be a bit silly to go past the S20FE for the price, especially since they downgraded the non-ultra S21 models this year. The S21 will still have a slightly better screen and non-main cameras, but whether that is worth a couple hunge extra for you is your call.