Engine wont start after it is heated up

What is your question?

So jeep will always start if it has been off for 10+ minutes or so. But if I drive it a few miles and then have to turn it off, and try turning it back on right away, it will just click once, and not start. Could that be a starter problem? I just installed new spark plugs. I did install a K &N air intake, but installed it perfectly, no loose wires or anything at all, so dont think thats involved.

What makes this problem better or worse?

I think it happens when the engine is fully at temperature and restarts when engine cools down