car wont start when cold outside but fine if over 40

What is your question?

Checked battery and changed gas filter along with plugs starter workes fine and can hear fuel pump on was told the coolent temp switch runs the starting of the car but this morn it tried to start than could not hear fuel pump and starter would not move only heard clicking under left side of car but was still told the coolent temp runs the brain that runs the starter and fuel pump and thats what tells your car how much gas to start with