Perhaps first see if the coolant temperature gets to the proper level. Not sure how they have a Mazda wired but there are often at least two sensors: one for the computer and another for the dash. It could be that your dash gauge gets its temperature from the computer, in which case you only have one.
Regardless, you want to see what the actual temperature is.
Do your radiator fans come on and stay on, even with the AC off, by chance?
Autozone or pepboys can check engine codes for free and they may be able to read what the computer thinks the coolant temperature is using that same method. Most more advanced scanners can do that.
If the engine’s coolant doesn’t get to proper temperature, the problem may be a stuck open thermostat.
While it isn’t a catastrophic failure, it will cause you engine to not run properly and efficiently. In colder climates, it will cause the engine a long time to heat up and in winter may cause you not to have heat in the cabin for more than what’s normal.
It the coolant temperature is indeed correct, it could be that the sensor used to feed the gauge is broken or somehow disconnected. Obviously, that would just be a readout problem, an annoyance.