Temp sensor failure?

First thing: you have a gen 3, where the engine coolant passes by two different temp sensors. Either one can light the overheat light on the dash.

Second thing: the overheat light on the dash usually doesn't mean a problem with the temp sensor. Usually it means the temp sensor is doing exactly what the temp sensor was put there to do.

So if it's saying stuff's getting too hot, the first order of business is to ask if that's true, why is it getting too hot?

Your OBD reader might be able to let you watch both temperature sensor readings. They come from different ECUs: one of the sensors is wired to the ECM, while the other is wired to the combination meter directly. If the reading you're watching is the ECM one and it is showing normal temps, then the abnormal readings are probably from the other one.

The other one is on the coolant coming back from the exhaust heat recovery heat exchanger in the exhaust.

Normally, that is only supposed to recover exhaust heat during warm-up. Once the coolant is warmed up, a thermostat-driven rod is supposed to move a valve so the exhaust now flows straight through the pipe and not through the heat exchanger. If that mechanism stops working right, the exhaust keeps on heating up the coolant.