98 Blazer temperature gauge broke?

The battery light come on so I went to the parts store to have them check the alternator. The idiot said it was fine and had me buy a battery. I made the trip home with everything working fine. 30 minutes later my mom went out to check it. The battery light was back on, showing 12v on the gauge while running, and the temperature gauge needle was hanging down. Today I have replaced the alternator. The battery light is off now and getting 13-14v on the gauge but the temperature gauge needle is still hanging down.

Is there a fuse or something for it? Or is it just broke? How can I check it/fix it?

what do you mean hanging down. Is it just pointing straight down? If thats the case, most likely the shaft has come off the actual shaft of the guage. Dissconnect the temperature sending unit at the engine and see if it moves. The sending unit is located at the thermostat housing, facing to the front. Its also used for the PCM too, so you could get a Service engine Light, but it will go out after you reconnect it.