1999 Mercury Mystique Car won't start when it's cold

Sounds to me like you need a new coolant temperature sensor. #1 cause of a cold start problem.

Are you sure you changed the engine/coolant temperature sensor? If you unplug the connector the temp guage on the instrument panel should stay the same, not peg all the way hot or cold.

Do you have a cold start injector? It looks like a fuel injector but not exact. There is one. Installed on your vehicle.

At the time it wont start check for spark and fuel pressure at your fuel rail.

Will it start if you have your foot on the throttle about 1/4 while cranking?

Has the fuel pressure been checked on cold mornings at the fuel rail, right away? Not after its been run but right when the problem is occuring?

Also check for vaccum leaks on all hoses and around the Intake manifold when you get the vehicle running if its warm, spray a can of carb cleaner on the vaccum lines and base of the manifold, if idle changes you have found a leak.