Car Does Not Start

I have a Toyota Corolla LE, 4 Cylinder, 1992 with about 180K miles and it is well serviced and I am the original owner. Recently the car starts fine but sometimes does not start unless I push the gas pedal all the way to the bottom. I also noticed that when the temperature is below 40 the car will not start, but when the temperature is above 50 starts okay, but then starts randomly starting okay or not starting at all. Can someone advice what kind of service, repair or part the car needs? I prefer suggestions or comments first rather than just go with the dealer and spend a fortune with them in trying to figure out what the problem i. Thank you.

I’d say coolant temp sensor if I was to give you a guess. If it was reading high it would not enrich the fuel during cold start.