My warning light for low coolant comes on all the time, even when the engine is cool and the radiator is full.

Dear Car Talk | Jul 01, 2003
Dear Tom and Ray:
I think I have a problem with my 2001 Ford Escape. My coolant-level light usually stays on, whether the engine is cool or has been running for a while. The level in the overflow tank is at the "maximum" line all the time, and unless I am totally lost, there is no fill cap on the (really thin) radiator itself. The temperature gauge never rises above halfway. Is this a blockage problem? -- Steve
RAY: No. A blockage problem is what happens when my brother eats two entire bags of Newman's Own organic pretzels in one sitting. What you have, Steve, is a sensor problem.
TOM: I think it's your coolant-level sensor. We replace a lot of these on Fords, so that would be my first guess.
RAY: There IS a radiator fill cap, but it might be on the engine itself, rather than on the radiator. And it's possible that your coolant level is low in the radiator (even if the overflow-bottle level is OK). So it's worth topping off the coolant before you try anything else.
TOM: But when that doesn't work, replace the coolant-level sensor. That should fix it, Steve.