BMW: Coolant level + temperature gauge, 318i 94/95, losing coolant, coolant level

Question
A few weeks ago, there was a small pool of coolant underneath my car. Took it to my mechanic, who said it was a seal, & replaced it. I kept losing coolant. He replaced the radiator. After that, I noticed that the temperature gauge would move (almost noticeably) towards the red zone. I stopped to let the engine cool & drove home, just a couple of miles. Mechanic's verdict: the new thermostat was faulty. It was replaced. Today -- the following day --, the coolant level  in the recovery tank was almost at the bottom, though there was no pool under the car.. I refilled it. Noticed that the temp gauge came up more quickly than usual to the normal operating range. I drove just a couple of miles, so I don't know if it would have gone again towards the red...
Help !!
P.S. The car has just over 63,000 miles

Answer
Water pumps don't fail very often in that car but anything is possible. It is also possible that your mechanic put the thermostat in backward so it wasn't working at all. The cooling system is sealed on that car so there is no overflow. If it was low this morning but there was no coolant on the ground that just means your mechanic doesn't know how to open the air purge screw on the radiator and bleed the system properly. Why don't we try and diag this ourselves and leave your mechanic out of it as long as possible. With a cold engine open the radiator cap and unscrew the purge screw. Fill coolant into the tank until it comes out of the purge hole steadily with no air in it. Screw the purge screw back in. Now top off the tank and leave the cap off. Have an assistant start the engine and rev to approx 2000 rpm. Watch for a steady stream of coolant to flow back into the tank from the fill hole area. If it does then the water pump is probably ok. If not the water pump is dead. Now watch for the coolant level to rise and drop approx 3-4 inches after it starts to warm. If It does this then the coolant is flowing every where. It should be ok to drive. It may need topped off as the engine warms so top it off running and rpm's still around 2000. Just remember to not contact the hot coolant, it burns badly and spreads quickly. And if your mechanic is really as dumb as you make him sound find a better one. You don't have to shop at the dealer for problems like this one but a bad mechanic can and will kill the engine with this overheating nonsense.