if it isn't properly cooled, and one of the most common causes of an overheating CPU is that the heatsink isn't seated correctly over the chip - added to which, many people use far too much thermal paste, and this can have exactly the opposite effect to that intended.
Make sure that you have seated the heatsink properly, and if you use thermal paste, ensure that there's only a thin layer between heatsink and chip. Check that the fan is running properly, and that there is no chance of the rotor fouling a cable as you close the case.
The reason that the CPU is recognised differently in the other machine is that the motherboard's Bus speed is wrongly set for that processor.
Are you sure the problem is caused by overheating - how do you know this?