The brief
The Passat had the temperature gauge climbing toward the red, steam coming from the engine bay, coolant leaking underneath, a burning smell from the engine compartment, and a temperature warning on the dash. He stopped driving it and brought it in, which is the right call, an engine that overheats shouldn't be run on. That whole list points at the coolant pump. The pump circulates coolant around the engine and through the radiator to carry the heat away, and when it fails it can leak coolant from its seal, which is the puddle and the steam, and it stops moving coolant properly, which is the rising temperature and the warning. An engine that loses its coolant flow runs hot fast, and a hot engine can warp a head, so it needs the pump changed.
The diagnosis
A pressure check and a look at the cooling system traced the overheating to the coolant pump, which was failing and not circulating coolant, weeping from its seal. The radiator, the hoses and the expansion tank checked out, so the pump was the fault. That's a pump replacement, with a fresh seal, rather than leaving a failed one to cook the engine.
The work
The cooling system was drained, the drive belt section released, and the failed coolant pump removed. A new genuine VW-spec pump went on with a fresh seal, the belt set back up, and the system refilled with the correct coolant, the air bled out the proper way, and held under pressure to confirm the seals were dry. A road test confirmed the gauge sat steady and there was nothing dripping.
The outcome
Gauge steady through traffic and at speed, no steam, no coolant under the car, no burning smell, and the level holding. The Passat went home with the cooling system back to spec. A failed coolant pump only stays failed, and the failure at the end is an overheat that can cost a head gasket, so changing it kept it to a tidy job rather than a far bigger one.