I don't recall which Mini it was but I swapped the CPU on it. Perhaps it was from core solo to core duo?
If your CPU is removable I would suggest removing the heatsink and cleaning out the old thermal paste and applying new.
Also blow out all the dust with compressed air (don't let the fan spin up, hold it in place)
Lastly on all of my Minis I attach small rubber feet on the bottom so that the bottom of the unit has air to flow by and not sit flat on a shelf.
Some people also put their minis on the side.
If you figure out the size of the fan etc I think you can also replace the fan with the same or another one with same specs.