Engine shuts off once it reaches normal running temperature?

What you described sounds like a failing crankshaft position sensor. When they begin to fail, they are adversely affected by heat. Once they cool off, they start working again.

Do me a favor. Take a look through this link and let me know if you feel anything mirrors what you experience:

https://www.2carpros.com/articles/symptoms-of-a-bad-crankshaft-sensor

If you haven't already, check to see if there is spark to the plugs when it won't start.

Here is a link that explains how that is done:

https://www.2carpros.com/articles/how-to-check-for-ignition-spark

If there is no spark, this is my first suspect. I attached the directions below specific to your vehicle for the replacement of the sensor.

Let me know what you find or if you have other questions.

Take care,

joe

See pics below.