On January 18, 2019, about 1530 central standard time, a Piper PA24, N6497P, sustained substantial damage when it was involved in an accident near Beechwood, Wisconsin. The private pilot sustained minor injuries. The airplane was operated as a Title 14 Federal Code of Regulations Part 91 personal flight. After 25 minutes of uneventful cross-country flight, the pilot noticed that the carburetor temperature gauge was in the “yellow” range. The gauge continued to move into the “red” range, which would indicate freezing. The engine began to lose power and the pilot pulled the carburetor heat knob to the full “ON’ position, set the fuel mixture to full, and turned on the electric fuel pump. There was no change in engine power, so the pilot checked the magnetos and switched fuel tanks from left to right. After pushing the carburetor heat knob in, the engine seemed to run smoother, but there was no increase in power. He pulled the carburetor heat “ON’ again, but the engine still ran poorly. By this time, the airplane had descended to 2,000 ft. The pilot trimmed the airplane for 100 mph. The engine remained running, but there was still no increase in power. The pilot pulled the carburetor heat “ON’ again, with no increase in engine power. The airplane was descending about 700 ft per minute and passing through 1,200 ft. The pilot made a distress call and announced that he was making an emergency landing. He configured the airplane for a gear-up landing in a field, during which the airplane sustained substantial damage to the fuselage. According to the carburetor icing probability chart, given a temperature of -7°C and a dew point of -14°C, it could not be determined if the airplane’s carburetor could have been susceptible to icing, because the dew point depression was not within the chart’s matrix. Damage to the carburetor assembly precluded determination of proper rigging; however, examination of the engine and fuel system revealed no anomalies. The carburetor heat control was found in the forward, “OFF” position.