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is the car automatic or manual?
I would suspect the issue has to do with the transmission failing to send the proper signal that it is in P or N when hot. Also the IVM could potentially be the issue
it could also be an issue with the immobilizer although this is less likely to be temp related.
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you would need to replace the tansmission position switch.
really the next step should be to replicate the issue with a factory BMW scan tool hooked up to verify the cause.
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