You can try moving the refrigerator out of its niche and vacuuming the coils. If that does not solve the problem, it's probably the thermostat gone bad and you need to call service and decide whether the cost of repair is worth keeping the unit or replacing it, keeping in mind that at 10 years old, things are going to start going wrong.
Thermistors you are just checking for resistance, check to make sure it changes as it heats up and cools. If you google it you can probably find where the range they are supposed to fall within.
Assuming it's cooling there is probably nothing wrong with the sealed system so you can eliminate the evaporator as an issue, usually it's more of an issue with the fridge not cooling that you start running into defrost problems etc.
To me I would make sure you are getting reading on the operating thermistors, assuming you do get proper readings change the board.
