Why will my 2001 Saturn start and run fine unless it is cold out

Have you checked the coolant temp sensor and connector?That sounds like the best place to start.

That car doesnt have a mass airflow sensor. Which coolant temp sensor did you replace?The top one with one wire or the bottom one with two wires going to it?Also did you inspect the inside of the connector to see if the terminals are silver and not green or blue?Those coolant temp sensors leak coolant into the connectors corroding terminals causing the sensor to miss read.

The top one with one wire runs the gauge the bottom one with two wires is for the computer. Are you sure he inspected the connectors?Also you have to make sure you replace the bottom one with the correct sensor.I have seen people get the wrong bottom coolant temp sensor and that causes issues. Most of the time when I see cold start issue on those cars is a coolant temp sensor issue. Try this next time it wont start try holding the gas pedal all the way to the floor while starting it see if it starts that way. Also when its hard to start and it finally starts does black smoke ever come out of the exhaust pipe?Any trouble codes?Have you checked for codes yet?

The water pump has nothing to do with it the black smoke is another thing you see with a coolant temp sensor issue. It totally sounds like a temp sensor issue. You dont have a scan tool that can read live data on that car like coolant temp etc?

The top sensor is a single wire that just supplies the ground to the temp gauge based on temp the ground value varies. The bottom one has two wires one wire has 5 volts the sensor changes resistance based on temp the pcm tells coolant temp by how much voltage the sensor reads across it

The third one the big one would be the oil sending unit.

Alright I just noticed you started the question 2001 saturn but on the cars info you put 1991 sc1. So lets get this squared away right now do you have a 2001 sc1?I had it in my head you had 1991 SC.

So when you have the no start is the security light on solid or flashing?

Sounds like you most likely have a bad pass lock sensor which is integral to the ignition housing. You need to get the body control module scanned for codes a auto parts store doesnt have a scanner to read those codes for free for you.