Hard Start after sitting for a few days, Runs fine after
 

Hey guys,
2000 Express 2500 5.0L 225k Miles
So this problem started randomly one day after driving home from work. Drove home, parked, no biggie. Went out the next day, no start. Cranks all day long with no success. Let it sit for a few days till I had time to dick around with it. Went out starts right up. Sweet all blue skys! Drove for a few days in a row. Had a few days off then same thing, no start. Pulling P1345 code. Crank/Cam correlation fault. Replaced both cam and crank sensors nothing. Go out one warm day ( its winter here). fires right up no problem! WTF! Drive it for a few days in a row no problem starts up everythings great. Leave it be for a few days same ****. Gas no problem ( you can smell it) Checked spark (Good) gets air. One weird thing it does is when excessively crankin it over it will randomly with cut the power then come right back on if you still hold the key to start. Seems to be very weather dependent. Went out this morning, after sitting for a day(Snow and rain 30 degrees) Tried to start it at 8am no go. Let it sit till 2pm (sunny 60s ) Fires right up. As long as I drive it everyday it will start regardless of weather. Recently did fuel pump, fuel regulator, crank sensor, cam sensor, ground strap. When it runs, its runs like a raped ape! That code makes me think it could possibly be a timing issue but does make sense that it will fire and run fine sometimes.I will also say that it has been going through coolant and there is no tomorrow. Makes me think it could be bad compression due to bad head gasket but no white smoke. It has been like that for a while. I checked the points on the cap and rotor, all good. Tried carb cleaner into the intake thinking not enough gas for start, ( worked in the past for weak fuel pump) but not this time... Checked power( battery cables, alternator cables, starter) everythings good. Could it be spark plugs? Its been about 90K since I have done them... Weirdest thing I have come across. Makes no sense to me hopefully one of you guys have an idea. Thanks for looking

Bad ignition switch or neutral start switch?
If you are losing coolant without a leak, it could be that compression is leaking into the water jacket and forcing out out the overflow.....

Potentially, My only thing is why would that be affected by temperature?

Maybe a loose wire in one of the two sensors that contracts in cold but expands when warm , I had it happen to my charging system because of the engine ground , like to have drove me crazy . Did you check for coolant in your oil ? When my head gasket leaked compression in to cooling system I could drive 45 minutes with no trouble then it would quickly start over heating because it blue coolant out the over flow tank. Just my 2 cents worth . Good luck.!

Thermal vacuum switches can cause temp related issues. Check all vacuum hoses.

And I'd check for codes again.