Car starts and runs for about ten minutes then dies. It wont start til it sits for about 15 to 20 minutes.

Have you done a scan as yet for any unresolved fault codes, not all codes will set a check light.

When it fails to restart, you need to find out what is missing to narrow down the possibilities if no touble codes are present.

https://www.2carpros.com/articles/car-cranks-but-wont-start

Try this link for an idea what to look out for.

If it is an air flow sensor problem, it would most probably have trouble code.

Since the problem occurs at a certain temperature and running time, I would lean more towards the Engine Coolant Temperature sensor.

Did the mechanic who checked the vehicle performaed a scan? If not, I would not take his word for it.

Replacing components without making any dignostics to confirm if it is the cause can be a waste of money and time.

Is the MIL indicating?
Most parts stores provides free scanning services so if you could get the vehicle them, you most probably can et the codes read.

If it is a fault with the ECT, you need to check if it is the sensor itself or wiring circuit. A sensor fault would be rectified when the sensor is replaced.

In one my previous post the link shows you what to look for when engine fails to restart. Go through them and see what is missing.

Which engine do you have?