So you're saying it's hard to start when engine is cold (anything under 195 degrees is considered cold)? And the starter cranks the engine at the correct speed, right?
The first thing I would do is press your foot down partially on the gas pedal while cranking the engine. If it starts faster that way, that's an indication that the engine coolant temp sensor is sending the wrong signal. Fairly common with Ford products. If the computer thinks the engine is warmer than it really is, it will cut back on fuel and make it almost impossible to start when cold.
You can scope out the sensor if you have the tools, but they're cheap (less than $25).