The airline transport-rated pilot taxied the airplane .5 miles to the hold-short line at the departure runway, where he intended to complete an engine run-up. According to the pilot, the right brake "didn't feel right" as he approached the hold-short line, so he completed a 360° turn to "test the brakes at a higher than normal speed." During the turn, smoke and then fire was seen coming from beneath the airplane. Once the airplane was stopped, the pilot and his passenger smelled smoke and then saw the smoke and fire. After the pilot and passenger safely egressed the cockpit, the airplane was destroyed by fire. The pilot stated that he thought the brake caliper was stuck, and while he expected the caliper to be smoking, he had not anticipated the fire.