Thermistor for Dometic RM 2510

I hope you solve the problem. I had a RM 2510 in a previous trailer, and while I liked it for dry camping since it only used 12V to fire the igniter, I had multiple problems with the thermostat & had to replace three of them, 2 for electrical failure & one for gas, but all kept it from cooling, not too cold. There is a mechanical connection between the diaphragm in the thermostat body & the electrical contacts that jammed off in my case; I suspect it could jam on.

I like the instructions for replacing it without removing the refrigerator, but I had to pull it all three times. By the way, keep the door gasket in good shape. You cannot replace it - requires the entire door replacement.

Thermistor is a capillary tube and part of the thermostat
Dometic 2007199009

Dual AC-LP Thermostat for RM2510

Here is one guys procedure for replacement: (w/o removing fridge)
Basic installation overview:
1. Disconnect 12v DC (battery) power and AC power completely.
2. Turn off propane at the tanks and drain lines by burning off at the stove.
3. Disconnect propane from master valve behind fridge.
4. Disconnect AC heating element from junction block, move junction block out of the way.
5. Take note and/or take pictures of the DC wire locations. Disconnect them and move them out of the way. I also had to remove a brass spade connector that was screwed into the frame.
6. Remove master propane valve. To do this you need to unclip it from its rotating clip behind the valve, unscrew the frame that holds the thermostat and propane parts in place to loosen it up, and remove the nut on its right side.
7. Remove propane thermostat intake tube on left side of thermostat, by removing its clip and using pliers to wiggle it out of the thermostat.
8. Slide thermostat to the left to remove it from the thermocouple on the right side. This should free it up some so that you can get to the AC spade connectors on the left side.
9. Take note of AC spade connector configuration, and disconnect from thermostat.
10. Rotate thermostat 90 degrees-ish so that it can be removed from the frame assembly. It should now only be connected to its capillary tube running up into the fridge.
11. Loosen screws inside fridge holding capillary tube to the fins. Push the capillary tube out through the hole through the fridge wall. Now you should be able to fully remove the old thermostat and its capillary tube. I was able to reach my hand up to where the capillary tube enters the fridge to pull it out from the back side. You may need a helper with small-medium sized arms and hands to do this without pulling the fridge, if you have large arms or hands. It's a tight fit.
12. Take note of rotation of D-shaped white thermostat ring, part of the rod that goes to the front of the fridge. Rotate new thermostat knob to roughly match orientation of the ring/rod. Or, you can rotate the knob from inside the RV to match the thermostat.
13. Replace O-rings if you have them.
14. Reverse the process to put everything back together with the new thermostat. Feed new capillary tube from back of fridge through fridge wall, attach to fins. Be careful not to bend or kink or force the capillary tube as it is fragile. Move thermostat back into place in its frame. Attach AC wires. Push thermostat to the right into thermocouple brass propane connection. Push propane inlet tube into left side of thermostat. Reconnect DC and AC wire connections. Push frame holding thermostat backwards and confirm on the inside of the RV that the thermostat knob is correctly aligned by making sure you can't turn it past OFF or MAX. Replace frame screws. Replace master propane valve connection, attaching it to the rotating clip. Reconnect propane pipe fitting.
15. Test for AC voltage at heating element when on electric mode with thermostat set to MAX, test propane fitting for leaks with soapy water, test for high flame on gas mode with thermostat set to MAX

Seems it has thermostat and/or the thermistor is built in with the thermostat. or maybe not--

https://www.rv.net/forum/index.cfm/fuseaction/thread/tid/29938148.cfm