Temp Guage issues

When there is a short circuit , the melt down occurs at the wealesy point in the circuit. That would be the copper trace on the circuit board. You could run a 12 volt wire directly to the gauge post and attach with a ring terminal but be forewarned ...
If the short still exists, further damage will occur.
I can only speculate as to where the fault is. My experience with these type gauges suggests the root problem to be inside that gauge.
Aftermarket gauges will be the least expensive solution.
If you want those factory gauges to work perfectly just send the entire instrument panel to me and i'll fix it. Warranty on my work is one year but after nearly 6 years I haven't had a come back yet.