car has to be push started on 1998 Saturn SC1

car has to be push started but once the engine is run for a while i am able to turn the car back on with just the key. what would cause this?

Asked by for the 1998 Saturn SC1
A couple of possibilities could be;

1-Clutch safety switch
Check voltage to small wire at starter with clutch pedal pushed
down and key turned forward.

When engine is hot,starter might be making a better connection
in the solenoid.