are you sure is the cpu gone, because the hard ware is got the over heat cut out system.
to protect the pc, if the fan don,t work properly and that will also cause that specially with amd cpu because amd cpu temperature is higher than intel cpu.
It is true the overheat cutoff could stop your fan running. The first step is to verify the fan is still in working condition. If the fan was bad, replace it to find out the old cpu still good or not. If the fan is good, check out any reset. The question about what is the better choice for the replacement of the AMD cpu? You have to check out the motherboard specifications to find the options for it. AMD's cpu characteristic is easily destroyed by overheating. More helps could be provided if you could post the more information especially motherboard type numbfer.