More often than not, what is perceived as water not circulating is not seeing the water in motion when the radiator cap is removed. On some radiators, you'll never actually see the water in motion. But on most, if it's not in motion, the thermostat hasn't opened yet.
If the radiator is full of coolant and the temperature gauge climbs very high, accompanied by other more reliable evidence of engine overheating like pinging (guages and their sending units can go bad) and steam coming out of the radiator eventually, or the radiator is cold but the engine is hot, it's usually a "stuck" thermostat, or one that isn't opening.
Personally, if I suspect this, I remove it, note the temperature at which it's supposed to open, put it in a pan of cold water with a meat or candy thermometer, put it all on the stove and bring the temperature up until you phycially see the thermostat open. Look at the thermometer. Right temp? It's a good thermostat but make sure it doesn't go in backwards or it'll be reluctant to open. If it's opening at a much higher temperature or not opening at all, replace it.
Three more reasons water might not circulate and I'm just throwing them out here because though they're pretty intuitive, they're still technicall reasons water might not circulate:
1. The water pump isn't being turned by the accessory belt.
2. There isn't enough water in it. Typically if your temperature gauge goes up and you turn on the heater and get only cold air, you're low on coolant.
3. The engine isn't running.
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