'92 car - low coolant alarm

Hey guys, i'm getting a "low coolant" light, and the annoying alarm lately. Only when I first start the car in the morning, ~40*F outside, parked on say a 7* slope uphill. I made it out of my driveway the first morning, the chime went off, so I pulled back in. I shut 'er down and popped the hood:

- Reservoir is full
- Rad is full

Same thing the next day (this morning). I shut it off and restarted it and it was ok. I had the heater on when the car started as well.

Where is the low coolant sensor located? Block? Is it (easily) replaceable? Is this a parts store part?
How does it measure, and set off the alarm?

Thanks