Freelander 1 Cooling Fan running after switching off

I have recently replaced my gearbox solenoids. Since undertaking this work, I have noticed that the cooling fan runs for some minutes after switching off the ignition. Maybe just a coincidence, but it did not do this before the gearbox work. I generally understand the pre-conditions for the fan to run for a few minutes. However, I'm surprised that the cooling system would get hot enough for this to happen after 10 minutes of quiet suburban running on a low 20's deg C day.

I guess it could be the fan clutch, thermostat, clogging in the cooling system, water pump etc

What I'm looking for is some advice on a step by step process of elimination to determine the root cause of this symptom.

Note: Since posting this, I have noticed that the fan tends to run on when I have been driving with the Air Conditioning on but not when I have not been using the Air Conditioning. The coolant guage sits constantly in the middle position.

have yer looked at the coolant temp with a diagnostic to see what the car thinks the coolant temp is?