There's a vac line connection from the intake (near the EGR valve) to the turbo boost sensor on the firewall.... check that first. Broken line means no boost signal to the ECU and no extra fuel.

Your car would've been running normal boost with way less fuel than necessary, aka running lean... leading to higher engine temps. Can't explain how it fixed itself, though.

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99 E300 TD -- sold
01 540i 6 spd