My car started overheating after a few minutes on the freeway today. Nursed it home (it cooled more when running at speed) and opened the bonnet to find the fan not running. I bridged the ground and fan terminals in the diagnostics box and the fan ran. This then appears to be a case of a faulty thermoswitch (the plastic top half actually snapped when I went to pull the electrical assembly off the top of it). I thought I would confirm this was the only issue and ran the car after it had cooled down a bit (was running just over half way on the temp gauge), bridged the fan again so it would run, but the temp continued to climb. This leads me to believe the fan is not the only problem

I fitted a new water pump during its last major service and the car has not had any issues since, so I doubt the water pump is the issue. Water seems to be moving between the overflow and the radiator, so there is no blockage there. It also has a relatively new radiator cap (fitted at the same time as a new radiator top).
Any suggestions on other possible causes would be appreciated, as I am stumped! I will try to find a thermoswitch to fit tomorrow, but as the temp kept increasing after the fan was manually ran I think this may not be the major problem.
Thanks