There is a huge difference between went back quickly and instantly recovered.

If the bug happens the actual engine temp is normal the gauge is just reading wrong and will instantly return to noon upon restart.

If there is an actual problem with the cooling system a restart will not reset the temp gauge. If the needle is right of noon upon restart and it takes any time to recover it's a different problem.

Temp high that recovers on its own hints at a sticking thermostat.

Use test 7 to monitor temp live and drive that same route to try to reproduce.

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2011 E70 • N55 (me)
2012 E70 • N63 (wife)