Okay, I hear the main relay is notorious for temperature affected starting, but the thing is, my symptoms are opposite of what other people's symptoms are.

For most people, the car has no trouble starting cold, but warm it has trouble. For me it's opposite. When my car's warm, the engine starts perfect, on the dot after a few turns.

When it's cold, the starter makes weird noises and even though the engine sounds like it wants to start, it won't.

My first assumption was:
Main relay
or
Coolant temperature sensor maybe?

The last would be bad starter, because if the starter was going bad, I'd think the car would experience problems starting even when it was warm.

I had to push start last night, but tonight it was a little colder. Tonight it was about 75-80 outside, instead of 85-90 which it was last night. During the day, 105 degree-ish the car has no trouble starting at all.

Car: 1993 Civic EX
Engine: D16Y8 with Y8 Dizzy wired to EX harness, P05 ECU (Saving money for a swap so I didn't want to buy a P28, rather save gas with a CX fuel map)

Thanks for any help guys!