engine cold, remove radiator cap. start engine. soon as the engine gets warm, at some point, the thrmostat should open and you should see flow. but be careful. once the thermostat opens, there maybe a rush of coolant. don't wanna get hot stuff on your face.
do have someone sitting in the car to monitor the temp gage. iffin sets to 220 w/o the rad showing flow, shut her down. either the thermostat has failed or the water pump is in Q. thermostats are cheap. and if there's no signs of coolant leaking around the water pump, and it'se pulley does not wobble or make moise, the water pump *maybe* for now, assumed good. and one would change the t-stat.
hard to tell, but if the rad shows flow, water pump passes a visual, the "engine" temp gage itself maybe bad. or have some air trapped around it(bleed system).
so technically, there are a few things it could be.
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but if i were to guess on one thing, i'd be right there with Scott and Pilsner Man. t-stat issue. and it's the most common cause.
thumbs to both Scott and Pilsner Man. the option for thumbs is not functioning for me. so pls consider it done.
Check all the prior answers to your question. If they all pass then you "might" have a stuck sensor or the wire going to the sensor is grounded. A wire can easily get pinched which would make your gauge/light show as hot. Rare to have a sensor go out, but it does happen.
You didn't mention what this is on. Vehicle year, make, model, engine,... would be helpful for us to help you out.
The sensor for the gauge is on the engine block, not the radiator. If the radiator is not hot you might not be circulating coolant properly, ie: thermostat is stuck closed.
The thermostat isn't opening, or your coolant is very low.
