The fan is operated by a bimetallic thermoswitch which screws into the body of the radiator. When the coolant reaches a certain temperature the switch turns the fan on to draw air through the radiator (eg. when sitting in traffic with no airflow through the radiator). Thermoswitches often fail Traci, then they suddenly won't switch the fan on. The temperature gauge then goes very high until the car starts moving forward and air passes through the radiator again. In that case, a new thermoswitch costs about £12-15. Your son will have to drain some coolant from the radiator then unscrew the old switch, fit the new one then top the coolant up again.
However, new thermoswitches can be defective. That was the case with my car a few years ago so I simply wired the fan directly to a switch I fitted on the dashboard. Now I just keep an eye on the temperature gauge then flick the fan on if I see the temperature start to rise in traffic.
If your son has removed the thermostat then the car should run much cooler than usual. If it's still overheating then I would suspect a blockage in the cooling system, either an airlock or just muck and rust. It could also be the radiator is very old and needs replacing, especially if it's been in the car since new. Places like Halfords do sell bottles of radiator flush fluid so that might be worth a try. Otherwise the problem will probably be solved by a new thermswitch or a new radiator.
Good luck.