The brief
The 318i was running hot, the temperature climbing higher than it should, coolant disappearing, puddles under the car, and a whine or grind off the engine bay, with a dashboard warning. The owner stopped driving it and brought it in, which is exactly right with an overheating engine. That list points at the water pump. The pump circulates coolant through the engine and the radiator so the heat actually goes somewhere. When it fails, the bearing gets noisy, that's the whine and grind, the seal weeps coolant, that's the loss and the puddle, and the impeller stops moving enough water, so the engine overheats. While the pump's out the thermostat gets done with it, it sits right there and a sticking thermostat causes the same symptom. A failing pump only gets worse, and an overheat can cost a head gasket, so it needs doing.
The diagnosis
A check of the cooling system traced it to the water pump, the bearing rough and the seal weeping, the impeller not moving water properly, so the engine couldn't shed heat. The radiator, the hoses and the rest of the system checked out, but the thermostat was getting renewed alongside as a matter of course given the access. That's a water pump replacement with a fresh thermostat and new seals, rather than chasing a weep that's only going to fail harder.
The work
The cooling system was drained, the old water pump removed, and a new genuine BMW-spec pump fitted with a fresh seal, a new thermostat in with it, and the drive belt set back up properly. The system was refilled with the correct BMW 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 gauge sat steady through traffic and at speed, no overheating, no noise.
The outcome
Gauge steady, no coolant loss, the engine warming up on time, and no whine from the bay. The 318i went home with the cooling system circulating properly again. A water pump that's noisy and weeping only fails harder, and the failure at the end is an overheat that can take the head gasket with it, so changing the pump and the thermostat together kept it to a tidy job.