The brief
The Tiguan had an unusual squealing sound and the engine running hot, and the owner was prudent to bring it in for a diagnosis rather than press on, an overheating engine can do real damage. A squeal plus overheating together points at the coolant pump. The coolant pump circulates coolant through the engine and the radiator so the heat goes somewhere, and on this engine the pump comes as a module with the thermostat. When the pump's bearing wears it gets noisy, that's the squeal, and as it goes the impeller stops moving enough water, so the engine overheats. A failing pump only gets worse, and an overheat can cost a head gasket, so it needs replacing as the module, with the thermostat that goes with it.
The diagnosis
A check of the cooling system traced the squeal and the overheating to the coolant pump module, the bearing rough and noisy and the impeller not moving water properly, so the engine couldn't shed heat. The radiator, the hoses, the drive belt and the rest of the system checked out. That's a pump module replacement, with the integrated thermostat going along with it and a fresh seal, rather than chasing a noise and a heat problem that are only going to get worse.
The work
The cooling system was drained, the old coolant pump and thermostat module removed, and a new genuine VW-spec module fitted with a fresh seal and the drive belt set back up properly. The system was refilled with the correct VW coolant, the air bled out the proper way so no pockets were left, and held under pressure to confirm the seals were dry. A road test confirmed the squeal was gone, the gauge sat steady through traffic and at speed, and no overheating.
The outcome
No more squealing, the gauge steady, no coolant loss, the engine warming up on time, and no overheating. The Tiguan went home with the cooling system circulating properly again. A coolant pump with a rough bearing squeals and then fails, and the failure is an overheat that can take the head gasket, so changing the module kept it to a tidy job.