It sounds like your furnace is cutting out before it satisfies the thermostat temperature set point.
It could be several things that cause this but we will start with checking the basics. Have you checked the batteries in your thermostat if it uses any? Remove the thermostat cover to see.
Also check to see if it is a flame sensor issue.
The flame sensor is a small thin steel rod that is straight or L shaped and is located near the pilot igniter or in the path of the burner jets. Locate it, remove it, and clean it with a piece of emery cloth or sandpaper very good.
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