Engine temperature warning light turned on?

This red warning light came on suddenly yesterday, telling me to stop driving. I was only a road away from home, so I left the car engine to cool, and later added some extra coolant and engine oil - although their levels were NOT low. I've tried it again this morning, the car having been overnight in the garage, and even though I just start the engine, the light comes on and suggests it is over-heating, which is impossible as the engine is stone cold.

I can find no leaks or problems with anything else and suspect it may be a sensor that has failed. Any ideas? Is it safe to drive it to a local garage?
Thanks, Martin