Typically catastrophic overheat is when the gauge spikes due to major component failure, like the radiator getting a large hole the water pump or serpentine failing and it going unnoticed. Losing a hose can sometimes fall into this category if it goes unnoticed for long enough to cause damage.
That said, replace sending into/sensor. Should be screwed into the cover plate for the thermostat iirc.
Also, I didn't see it answered apologies if you did, is it actively overheating or is the gauge just overheating?
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