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I don't see your year or model but this could be the temp control itself, possibly the blend door motor or the blend door too. Most likely the temp control has been adjusted enough to "wear out" the resistance it provides in controlling the door motor.
When mine failed it was either full cold or full hot, nothing in between and would occasionally jump all by itself without moving the dash mounted ****.
Replacements are about $20 and easy to change after you get the dash trim pieces off.