After around 5 days of use,yes its cooler.
Never checked temps before but so far besides during the initial samsung switch, never felt the phone being warm to touch.
I don't game a lot so I can't comment on that.
Battery life especially standby time also improved.
Previously on my Note20U, can't last through a 12 hour shift at work with full 4g. Now from unplugged at 80% till finish work left around 20%. This is on full 4g with so so reception so if you are mostly on wifi/have good signal strength I expect you'd get better battery life.
To be honest, the most satisfying thing about the upgrade has been the battery life.
Other points that have improved
Screen - texts are sharper since we can run it at QHD instead of stuck at 1080p 120hz. Depends on people but it's actually noticeable for me.
Camera - even though both note 20u and s21u using laser auto focus, the focus enhancer mode that uses the wide angle for close shots works really well if you use the camera for close shots a lot. S20U has the worst camera experience

All in all am finally satisfied with my phone. After a year of going through the S20U then Note20U.
*I know the SD may have better performance/battery life. But can't bring myself to risk getting a phone with poor/no local warranty support. Have had good experiences with Samsung SC so far, S20U changed screen + camera module, note 9 changed camera module. All done within few hours with no fees.
Thanks for your detail explaination. The note20u having bigger square screen which I like the most. But I really cant tahan with the battery life and especially warm when heavy usage.
If I go for s21u, i will have to sacrifice the big screen and S-Pen. ... and of course fork out more money ...... not sure worth or not if just want to get better battery life.
I play few games only ... mostly play Tennis Clash ... and exynos990 getting very hot if I dont switch it to 60hz ... and throttled after 10-15mins ... very bad on n20u expensive phone.