Car problem? I hope someone can help!?

Hello, I have a 1998 jeep cherokee classic. My car runs fine the first time I start it, it turns maybe once or twice and kicks right in. Heres the problem, if I were to shut my car off before the cars temperature reaches 210, which is its normal warmed up operating temperature, it will not turn back on! I mean the thing will not even turn over. If it is at a dead cold sitting there for hrs, no problem but lets say I take a ride around the block and it reaches lets say 180 and I shut the car off, it will not re-fire for a long period of time. Heres the other thing I don't understand: Tonight I forget to let it warm up fully, and shut it off, ran into the store and back out, it was maybe 15 mins top. Came back out and I turn the key to the start position, and nothing, so I figured alright it is going to play games with me again. Eventually after about 20 mins of turning the thing from off to start it all of a sudden fired up on the first turn over. I know for a fact it is not the battery or the starter itself as they were both replaced recently. The problem is somewhere between the key and the starter. When I take it to my mechanic it never does it and it is getting really annoying having to wait for the truck to warm up every time. Does anybody know what could be wrong?

One additional detail if it helps, once the truck hits its operating temperature, I can sit out there all day and turn the thing on and off problem free. Also when I have this problem and the key is in the start position, I hear 2 quick clicks and nothing else reguardless how long I hold the key in the on position and I here the clicks every time I go back and fourth between on and start or off to start.

Thank you everyone for help! Lee