Well if you can read the current temp and the current setting I would think the battery or fuse would be Okay.
Is it the Coleman Mach Digital thermostat? Or do you have a newer rig with the "Multi Plex" system?
My Coleman does NOT have a battery. But it Might have a fuse... I never looked.
Let us know which thermostat you have first.
2017 Axis / 25.4: Big Foot Levelers, Aims 1200 Watt inverter, Ceramic Window Tint, Full River AGM 6V batteries, Front Hellwig Sway bar / Rear Track Arm, Safe T Plus Steering Stabilizer, PD 4655 converter, Hard Wired Surge Guard, WEboost + WiFi Ranger, LED Headlights/Driving lights, TPMS, Surge tank, Tornado flush, Viair Compressor