How much does temperature affect motor?

Could be carb related when cold but ignition related when hot? Coil getting heat soaked maybe ?
Its idling pretty high for a stock cam .

I can get it to idle lower in exchange for a little bit of an engine "wobble/shake" I can get it down to about 700-750 in park and itll drop to about 650-700 in drive but it shakes around more than I would like. At my current settings the engine idles really really smooth at start up.
I have also suspected maybe a faulty coil because I have no idea how old it might be but I want to exhaust all options before I start throwing parts and $$$ at the car.
Ill start with getting it real hot and then spraying around all the seals to see if the engine will react at all