Engine temp warning light?

My 2006 c3 has developed a fault whereby the engine temp warning light randomly comes on. It has only happened so far when going down hill! When i ve stopped the car as instructed the fan remains on for about ten mins then the problem has gone. There is no obvious signs of overheating e.g boiling . I have changed the engine temp sensor on top of the thermostat but that has not solved the problem . Someone told me if the engine management light doesnt come on the problem will not show up if i pay to put it on a diagnostic machine is this true HELP.