Could you tell me what parameters I should touch in the bios to "tame" the temperatures of the i7-10700K a bit?
You have several options.
-AVX offset. Auto is usually 0. AVX demands more power and heat when it kicks in. Experiment between -1 to -3. As you go towards -3, the power use should go down, but so does performance*.[AVX is faster than the normal SSE Instructions at the same frequency.]
-Cpu Vcore. You can use either Manual/Offset/Adaptive Mode, just don't leave it on Auto. Manual and Offset are easier to use. Ex: Offset Mode, and enter an offset of -0.050v. You may be able to go further than that, like -0.100v.
-Load Line Calibration. Can vary between mobo makers by a lot. [
Link to how LLC works] For most users, the low to medium LLC settings are as far as they need to go. The high to extreme settings crank needlessly higher voltage through and increase thermals further.
-Multi Core Enhancement/Enhanced Turbo. Some boards have it on by default. It's an E-Z overclock, but uses too much voltage. Leave it off... or don't, if you believe you can tame the Vcore.
-C-states. Leave them on.
-Intel Speed Shift/Speed Step. Leave Shift on, turn Step off.
Excluding the last 2, try not to change too many of the others at once. For now, see what tuning the Vcore does for you.