Malfunctioning Coolant Sensor?
 

As you can see in my sig, I have a 2001 VR6. 89,xxx miles.

Everytime I start the car, the coolant warning light comes on, beeps idiotically, and remains on for about 5 minutes before shutting off. I've obviously checked the coolant level and it is right on point. The temperature guage never fluctuates either.
Today the light came on again as usual, however never shut off or stopped beeping on my 20 minute drive to work. [:@]
I'm assuming it's merely a bad sensor.
Does anyone have any experience replacing this sensor or where the sensor is located?

Thanks in advance!