No it would not only a bad (ICM) Ignition control module or a bad injector would...
On the engine block, near the thermostat housing.
There is a sensor either in the coolant recovery jug or the radiator side tank that is defective.
There is a sensor in the side of the radiator that is most likely defective.
There is a sensor valve located inside the reservoir its may be bad
I have seen this before more than likely your coolant sensor has a internal short and needs to be replaced.
antifreeze is most common problem related to petrol engines misfiring. this can be cured by replacing the timing belt in addition to the thermostat and coolant temperature sensor. this will remedy 95% of misfire problems on most modern cars.
Check the coolant level and make sure that its full, and is not leaking down over time. If the system is full then the low coolant sensor is probably bad.
could be tps or throttle positioning sensor
Coolant temperature sensor circuit high. Check the sensor near where the upper hose attaches to the engine to see if plugged in.
coolant temp sensor is on the driver side rear cylinder head. If you look straight down upon the rear head you will see the connector plugged straight into it!goodluck.
Bad temperature sensor? Plugged or restricted radiator? Water pump not circulating coolant? Thermostat not opening? System airbound?
Follow the lower radiator hose from the radiator to the back of the engine. Where it connects to the engine, you will see wires plugged in to the sensor