On October 9, 1996, at 1845 central daylight time, a Dickson RV-3A, N3920P, was destroyed by fire on the ground after impacting a wire during a forced landing near Rosharon, Texas. The private pilot, sole occupant in the airplane, was not injured. The airplane was registered to and operated by a private owner under Title 14 CFR Part 91. Visual meteorological conditions prevailed for the personal cross country flight which originated from Houston Gulf Airport near League City, Texas, at 1810. No flight plan was filed for the flight. The pilot reported to the investigator-in-charge that he was doing "some formation flying and sight seeing" with a friend in another airplane. The pilot stated that "approximately 10 to 12 miles southeast of Houston Southwest Airport I pulled the power back to approximately 1,000 RPM in order for my friend to catch up with me." Approximately 30 to 45 seconds went by and the pilot advanced the throttle to discover that he had "no power." The pilot estimated that he was at 1,000 feet AGL and he decided to perform a forced landing. During the forced landing, the pilot reported not seeing a power line that ran across his landing area and the airplane's landing gear impacted the wire. The pilot reported regaining control of the airplane and continuing the forced landing. The impact with the wire damaged the landing gear and subsequently components of the fuel system. Witnesses observed a fire in the engine compartment area after the wire impact. After landing, the pilot immediately exited the airplane and the airplane subsequently burned. The pilot, who is also an aircraft mechanic with an Inspection Authorization, reported that he suspects that the aircraft's engine power loss was due to "carburetor icing." The temperature and dew point reported in the local area at the time of the accident place the ambient air well inside the possible carburetor icing area on the Icing Probability Curves Chart (see enclosed graph).