Hello I'm Neal and I am here to help resolve your issue. If I cannot help I will opt out and refer your question to another expert.
In my experience it is most likely going to be the crank sensor, when they start to go bad they can be temperature sensitive and they do what you describe. If it was in my shop I would try that next as there is no way to test it when it is intermittant like that. The sensor is only $25 to $50 depending on the brand you get, I would go with the $50 one myself.
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