Your desktop just for normal usage. It won't overheated coz the old processor won't generate so much heat as the modern processor. You can dismantle the heatsink with fan. For me, I will remove the fan out then wash the whole heatsink cleanly with water. Let it fully dry then install back the fan on top of the heatsink before apply thermal paste and install it back on top of the processor. It will give you best heat dispenser but if the fan's motor is not good and it give you slower fan. You can try look for the compatible fan to replace it or buy a new heatsink with fan that can mount up on your mobo.
Old desktop fan