Hot day No run.
 

On a hot day, my miata will start, run a short time, then shut down, Will restart when outdoor air cools down. On a cool day, no problem. It sounds and feels like car ran out of gas.

Just a hunch. Next time it happens, loosen the gas cap.

I already tried loosening the gas cap when car stopped running. It let off pressure, but car would still not start. My mechanic is suspecting fuel pump relay switch located under dash. when car stopped running, I jumped wires to get car home. The next day I started out with wires jumped, it was a hot day and car only ran for a minute.

I would start by checking that all connectors are fully seated, especially around the intake area(MAF, Throttle Body) and check the grounds, especially by the throttle body.

Maf?