Hi @sagarcena
If you mean the [https://www.partselect.com/PS11743106-Whirlpool-WP61001673-Cold-Control-Thermostat.htm?SourceCode=21&SearchTerm=AS22N8DE&ModelNum=AS22N8DE|temperature control thermostat] (part #WP61001673) it is a simple on/off switch that opens and closes at the desired temperatures turning the compressor on and off.
Here's the [https://www.partselect.com/Models/AS22N8DE/Sections/WIRING-INFORMATION/?ModelID=241401&ModelNum=AS22N8DE&mfgModelNum=&ManufactureID=1&Selected=48700&Position=9&mfg=Maytag&Type=Refrigerator&Mark=9|wiring diagram] that may help.
You would need to disconnect the power to the refrigerator and then use an Ohmmeter connected the thermostat and check if it was turning on when the temperature is above its set upper limit i.e. ~41°F
If the thermostat is faulty it cannot be repaired. It has to be replaced. Search online for the above part number to find suppliers that suit you best.