I’ve been noticing this phenomenon occur lately and I’m wondering if it could be indicative of a cooling system problem? As soon as I fire the car back up though, the temperature comes back down and the needle goes back to dead center. Has anybody here experienced the same thing?
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From Bruno’s site:

Why when I stop the engine and start it 5min after, the temperature needle is hitting the 3/4 mark?

• The phenomenon known as "heat soak" occurs when the engine is turned off. At this time, the combustion process is terminated. This terminates the momentum of the crankshaft, which in turn stops the turning of the water pump. As the coolant is no longer being circulated, the engine block and cylinder temperature increase for a period of approximately 3 to 10 minutes, depending on the engine design and additional components. During this time, the engine block radiates heat to the air surrounding the engine, which slowly cools the engine. However, the cooling process occurs slowly, and as a result, the temperature of the engine block transfers the heat to the coolant. The coolant temperature then increases, which in turn increases the pressure inside the coolant system. This is why the vehicle's coolant temperature gauge increases over a period of time after the engine has been turned off.

BMW E34 Website