The brief
Mr Lee's Golf had developed a serious overheating problem, the gauge climbing fast and the temperature warning coming up, so he brought it straight in. Overheating is one to act on immediately, because a hot engine warps the head and blows the head gasket in short order, and that repair is a big one. The water pump is what keeps coolant moving around the engine and through the radiator, and on these the pump runs an impeller that on a lot of them is plastic. Over the years that impeller wears down or cracks loose from its shaft, so the pump spins but barely pushes any coolant, and the engine cooks even though there's plenty of coolant in the system. A worn pump can't be revived, and the thermostat lives in the same housing, so the two get changed together as a module.
The diagnosis
The check found the water pump failing, the plastic impeller worn so it wasn't circulating coolant properly, which is exactly why the engine overheated even with the coolant level up. The radiator was flowing and the rest of the system was sound, and the thermostat in the same housing was due alongside the pump. That's a water pump and thermostat module replacement, plus a coolant flush and bleed since it had been run hot.
The work
The cooling system was drained, the old water pump and thermostat housing removed, and a new genuine VW-spec pump and thermostat module fitted with a fresh seal, the drive belt or chain that runs it checked and refitted to spec. The system was refilled with the correct VW coolant, bled the proper way so no air pockets were left, and pressure tested. A road test, including time idling in traffic, confirmed the gauge holding steady and the engine warming up at the right rate.
The outcome
The gauge holding steady on the move and in traffic, the engine warming up at the right rate, no temperature warning, and the coolant fresh. The Golf went home with the overheating fixed. A worn water pump only gets worse, so replacing the pump and thermostat together and refreshing the coolant put the cooling right before the heat did any lasting damage.