Which board that is and does it have official support for coppermine and what kind of voltages it can provide? This is what matters and not just some bios compatibility.
That CPU is relatively high power to begin with, little over 30W or so at 1,45V-1,5V. Coppermines have 1,6-1,75V and Katmais 1,93-2,1V. If your mobo voltage regulator can’t go lower than 1,8V for example, like many 440BX boards can’t, you are blasting that CPU with too high voltage and it draws significantly more power, something like 40W. That will put the that VRM under strain and it is no wonder that regulators start to heat up, it wasn’t designed for those kind of loads and it is easily 20% more than the highest Katmai has.
Tayeh caps are bottom tier plague era junk, right down there with GSC, and I would replace them immediately no matter how they look. I don’t think they are the source of your heating problems. Without you providing more information, my bet it is that you have relatively high power CPU which you are overvolting like crazy and powerdraw is out of spec for that board.