If you're referring to the coolant temperature gauge in the instrument cluster, the most likely cause is a dead gauge stepper motor. Since this is a common problem that also affects other gauges, the best solution is to buy a packet of four or six (depending on how many gauges you have) new x27 stepper motors from eBay. Just type "05-09 Mustang gauge stepper motor" in search box. Don't be put off if they're made in China. They work fine.
If you're handy with a soldering iron, you can desolder the old ones out and resolder the new ones in yourself. I did all six of mine last year in little over an hour. Just take your time and be patient. If you'd rather pay someone else to do the job, either a guy in a local electronics repair shop could do it for you, or you could send the cluster to a specialist in that type of repair and pay about $100.