1) Update:
"59-60c in my bios which seems really high"
Uh... it is, but your stress tests are fine. Your BIOS settings don't make sense (and you didn't mention that before) as that's idle temperature and it should be closer to 30-40degC range. That seems more like a REPORTING ERROR to me as there's absolutely no way it can be that high barring the fan turning right off.
AND, you said initially it was 35degC in (Windows idle I assume) so...
2) BIOS UPDATE:
See if a newer version exists. You don't have issues in the OS so it's really not required. It may or may not fix a reporting error if it exists.
3) Did you OC, or just use defaults?
- it sounds like it's just default, and it works fine in Windows so I wouldn't mess with it. (note some settings may prevent your system booting if you change them, usually CSM, UEFI, secure mode etc)
- if you did OC you could try going back to DEFAULT settings, then enable XMP (and make any other changes you know of that are necessary) and save, reboot.
4) NOCTUA FAN: again, this is really to reduce noise. If that's not an issue you can ignore this. (also handy if considering case fans. Even if you want a different BRAND you should be aware that case fans and CPU fans are different in how they push air, and also the RPM range, some boards don't support 3-pin though yours probably supports both 3-pin and 4-pin.
will be 4-pin, PWM fan anyway so no worries. Just shut down and change fan (clips).
**So the NF-F12 appears to be the best 12cm, Noctua fan for you (see above link). It also has an LNF adapter so you can reduce fan speed, and I would actually use it. WHY? It helps reduce the fan speed thus noise when the computer first starts up. You absolutely do not need full RPM once you setup your fan profile.
The range I'd choose would be probably about 40% max (600RPM) to 70% max. Run Prime95 and use 80 or 85degC as the worst-case so put the RPM at the LOWEST speed that maintains that for ten minutes.
(a good case fan often sees very minimal CPU/GPU benefits going above 700RPM but it varies on several factors.)
$20 fan:
https://www.amazon.com/Noctua-NF-F12-PWM-Cooling-Fan/dp/B00650P2ZC
So..
#1 (optional) - record noise (or try to remember) with Prime95 at 80degC (and the fan profile adjusted to maintain that)
#2 shut down, install fan
#3 optimize fan profile with the motherboard software (i.e. 40% RPM up to 50degC, then ramp up to 70% at 80degC, and 100% at max RPM). Just an example. (I try to keep the fan from changing speed in light usage so 50degC is probably a good point, and 700RPM with that CPU cooler is almost silent anyway).