You have a short in thermostat wiring or in the control circuit wiring
Could be on 12V DC wire to t-stat from battery (RED)
Could be on 12V DC wire from t-stat to furnace (WHITE)
Could be on 12V DC wire from t-stat to AC control (Yellow)
Could be internal short t-stat
First place to start....remove t-stat and inspect for burnt contacts/loose wiring/wires touching
Here is a service manual for your t-stat........
LINK
Is it time for your medication or mine?
2007 DODGE 3500 QC SRW 5.9L CTD In-Bed 'quiet gen'
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US NAVY------USS Decatur DDG31