Why would a car start when cold but not start and cranks only after it's been driven awhile?

I'm not sure I understand the question but I do know this. If your car will start when it is cold, yet after driving it for awhile, you shut it off and then go to restart it and it wont start you need to have your starter and starter solenoid checked. Its happenened to me on 2 different cars. It seems that when the starter gets to hot it just jams up or freezes up and won't crank over the engine. Yet if the car sits for a little while it cools down and then seems to work just fine. Its defineately a sign that your starter and/or solenoid is about to die. Pull it out and have it checked.(auto zone will do it for free, its called a load test) There's a good chance that's your problem, if I understood the problem correctly. Good Luck, hope this helps.

Mark H.