When an engine coolant temperature sensor has gone bad your car is usually hard to start and the engine will run rough for awhile until the engine is warmed up and/or it will stall soon after starting.
The engine coolant temperature sensor tells the computer how cool or warm your engine is and lets the computer know to tell the engine how much fuel and air it needs to get up to speed.
Before replacing the coolant temperature sensor check the connection to the coolant temperature sensor as I've fixed some vehicles that were thought to have a bad coolant temperature sensor by unplugging and plugging the plug back into the coolant temperature sensor.
Although rare sometimes the plug comes loose or if someone was working under the hood maybe they temporarily unplugged it to get at something else and then didn't fully plug it back in or didn't plug it back in at all.
I've found some coolant temperature sensors unplugged and plugging the connector back in fixed it.