The brief
The 520i had coolant leaking from the water pump housing, with puddles under the car, visible stains and drips in the engine bay, the temperature climbing, and the heater feeling weaker than it should. He brought it in before it overheated outright. On these BMWs the water pump is electric, and it sits in a housing that's part plastic, which ages and cracks over time, letting coolant weep out, which is the puddles and the stains. Lose enough coolant and the level drops and the engine can't shed its heat, which is the rising temperature and the weak heater. An engine that loses its coolant flow runs hot fast, and a hot BMW engine is one you stop driving.
The diagnosis
A pressure check traced the leak to the water pump housing, cracked and weeping, with the hoses, the radiator and the expansion tank all checking out clean. The pump itself was the same age and the same wear item, so it goes in with the housing. That's a housing-and-pump replacement, with the thermostat in the same circuit done at the same time, fresh seals throughout, rather than being back in here when one of the others lets go.
The work
The cooling system was drained, the failed water pump housing, the electric pump and the thermostat removed, and new genuine BMW-spec parts fitted with fresh seals. The system was refilled with the correct coolant, the air bled out the proper way following the procedure for the electric pump, and held under pressure to confirm the seals were dry. A road test confirmed the gauge sat steady, the heater worked, and there was nothing dripping.
The outcome
Gauge steady through traffic and at speed, no coolant traces, the level holding, and the heater working again. The 520i went home with the cooling system back to spec. A cracked plastic housing only cracks further, and the failure at the end is an overheat that can cost a head gasket, so changing the housing, pump and thermostat together put the whole circuit right in one visit.