My car has been running well enough since the shop replaced the thermostat that was apparently the root cause of some previous problems, but it's started to get hot again.

First off, they took the thermostat controller thing out of a XJ8L Vanden Plas and popped it my XJR. Are the thermostat controllers the same for both cars or could that be the issue?

I drove the car lightly today, returned home and parked it in the garage and the fan ran for about 4-5 minutes after shutting it off.

It sat in the garage for about an hour then I started the car and backed it up maybe 10 feet into the driveway then shut it off. Again, the fan ran for 5 minutes just from turning the car on and shutting it off.