My car turns on when cooled or cooled down.

Hi,

There are 2 common causes for "warm start" & "warm stall". The EVAP Purge valve (n80) and the Engine Speed Sensor (crankshaft position sensor).

When the engine doe not start, it turns over OK?

The N80 valve can stick open. When that happens, Gasoline fumes from the Charcoal Canister/Gas Tank fill the intake manifold. This causes a
rich air/fuel mixture the next time you try to start the engine.

Let me know what engine size you have and I will tell you to location of the N80 Valve so you can check it.

The engine speed sensors fail when they get old. At first they fail when the engine gets warm/hot. At which point the engine stalls or the engine
does not want to start (after coming back to the car from shopping). Once the sensor cools off, the engine will start again. When the sensor fails
completely, the engine won't start even when the engine is cold.

The Speed Sensor "should" set a Fault Code in the ECM Memory. The N80 Valve may or may not set a fault code.

There are other things that could cause similar no-start / stalling issues, but these (in my mind) are the two most common ones.

Thomas