More likely to be caused by a cracked windshield!
Rough idle means a misfire. The Check Engine light should be on and a diagnostic fault code will be stored in the Engine Computer that will direct you to the specific cylinder. If you don't have a code reader, many auto parts stores will read the codes for you for free.
I guess a defective coolant temperature sensor could cause hard starting, but the way they fail will usually cause over-fueling well after the engine is started. That means black smoke out the tail pipe and poor fuel mileage. Ford has a lot of trouble with their coolant temp. Sensors but failure on Chrysler products is pretty much unheard of.
The thermostat doesn't even come into play until the engine is warmed up. The engine will start fine without one and run perfectly smooth.
How long since the spark plugs were replaced?
Caradiodoc
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Saturday, January 22nd, 2011 AT 5:27 PM