I assume this is a top mount freezer model with automatic defrost. If so, there is a fan that blows cold air from the freezer evaporator down into the refrigerator compartment. The fan may have failed or the return air duct is blocked.
This can occur if the drain pipe/pan becomes iced up due to a blockage. You need to remove the freezer evaporator cover to check.
You could have a defrost element failure and the first symptom is poor ref compartment cooling followed by gradual poor freezer cooling due to icing. Not likely to be any problem with the thermostat.
Maybe some photos or a model number may help.
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