I have the exact same problem! It's a constant balancing act between layers when backpacking. I'll wear only a patagonia mid layer merino wool long sleeve shirt hiking in 30F degree weather just to keep from sweating too much. I'll have my fleece layer and down jacket easy access so when I stop I can throw one or both on to stay warm. I'll constantly take off and put on my beanie for the same effect. When it's colder out like -20F - 0F I can't push myself too much because I will start sweating and it's too cold to be exposed. It's annoying but it is what it is. Just have to find a medium pace that won't overheat my body and cause too much sweating.

For mountain biking I just accept I am going to be drenched and if need be bring a second shirt/base layer during cold rides. Always have a change of clothes in my car too so I can put warm dry clothes on immediately after a ride.