You need to do some checks on the cooling system. Pressure and temperature are directly proportional to each other. As the engine warms up some of it's heat is given off into the cooling system. The coolant expands as it gets hot and so the pressure rises. If the temperature falls so does the pressure, therefore the pressure in the cooling system is regulated by the temperature. The coolant pressure cap is an overall safety valve, and lifts if the pressure exceeds the rating stated on the cap, usually around 15psi. Another valve in the cap will open as the engine cools when it's not running. This allows air in at the top of the system to prevent hoses being vacuumed flat as the coolant contracts.
Make sure the water pump is in good condition and can properly circulate the coolant. The operation or otherwise of water pump has nothing to do with cooling system pressure. It's a centrifugal pump that aids circulation, that's all. Cebtrifugal pumps are used in high flow and relatively low pressure applications.
Make sure the cooling system is properly bled. BMW's can be a bit awkward to bleed. Remove the plastic screw at the top of the radiator when the engine is cold. You will achieve nothing by running the engine with this screw removed, so top up the system until no more air comes out of the hole.
Use a cooling system pressure tester the attached it to the radiator filler in place of the filler cap when the engine is cold. Start the engine and allow it to warm up. If you see a rapid increase in pressure whilst the engine is cool then you have a cylinder head gasket issue, otherwise the pressure should gradually increase as the temperature rises. When the thermostat opens coolant will flow through the radiator giving off heat by moving onto the fins and then into the air. The second law of thermodynamics, 'heat always seeks out cold areas' sees to this. As this happens the pressure will fall slightly, before rising again as the engine temperature continues to rise. When the engine is fully warmed up the viscous fan coupling will lock up and the fan speed should increase, thus drawing air through the radiator. Once again you should see a reduction in pressure as the temperature reduces.
This hopefully should help you to diagnose your problem. Remember to allow to engine to cool suffiently before you remove the pressure tester to avoid personal injury.
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