A bad coolant temperature sensor can cause rough idle, hard starting, engine stalling, engine overheating and even black smoke can come out of the exhaust due to a bad coolant temperature sensor.
A bad coolant temperature sensor can also cause decrease in fuel mileage and your check engine light to come on.
A coolant temperature sensor tells the computer when the engine is warmed up or cooled down and adjusts the fuel to air mixture ratio for a proper running engine.
Having a properly working coolant temperature sensor is essential to a properly running engine.