THE STUDENT PILOT WAS DEMONSTRATING HIS ABILITY TO MAKE 3 LANDINGS TO MEET THE FLIGHT REQUIREMENTS FOR A PRIVATE PILOT RATING. THE FIRST 2 LANDING WERE WITHOUT INCIDENT. AFTER THE THIRD TAKEOFF, AN INCREASE IN THE WIND VELOCITY WAS ENCOUNTERED. FOR THE THIRD LANDING, AN OPEN FIELD WAS SELECTED. THE FIELD WAS DOWNWIND FROM A RIDGE AND A HIGH VOLTAGE POWER LINE. ACCORDING TO THE CREW MEMBERS, A SEVERE ROTOR OR VERTICAL WING CURL WAS ENCOUNTERED WHICH COLLAPSED THE SIDE OF THE ENVELOPE, ALMOST A THIRD OF ITS VOLUME. REPORTEDLY, THIS OCCURRED AFTER THE LANDING APPROACH WAS ESTABLISHED. THE STUDENT TRIED TO COMPENSATE FOR THE LOST HEAT AND LIFT BY USING BOTH THE MAIN AND THE AUXILLARY BURNERS. BUT WHILE STILL DESCENDING WITH POWER LINES AHEAD, THE PILOT ELECTED TO DEFLATE THE BALLOON FOR AN IMMEDIATE LANDING. HOWEVER, THE ENVELOPE DRAPED OVER THE LINES AND STARTED BURNING WHEN THE LINES ARCED.