2008 Ford Focus temperature gauge jumps up

 Ford Focus

Temperature gauge jumps up

After I have driven my car, the next time I start it, the temperature gauge jumps up and the car smells like something is hot. It will also rise if I am idling at red light or when the key is on, but the car is not running. After a few seconds, the gauge will start to drop and return to normal temperature. The coolant reservoir is full and I cannot find a reason for the temperature gauge to be spiking. It does not do it during the winter, when the weather is cold or the first time I start my car, only in warm weather and after I have already driven the car that day.

The plastic tubing around my battery cable also melted off. I am not sure if this is related, but it seems unusual. Any ideas what could be causing the spike in the temperature gauge and the hot smell?

temp gauge