No ignition switch when warm ???

[PARKERRS]

Make sure the poles on the new solenoid are the same as the old and not reversed. Then I would check the brushes in the starter.It could be the solenoid is stuck or the brushes, an old parking lot trick was to tap the starter with a hammer while someone turned the key. Be very careful trying that one you don't want to get run over by your own car if it is in gear. This only works with old style GM starters, the new ones and some of the high torque models use earth magnets and rapping on them with a hammer will destroy them internally.

Tommy