During a proficiency flight check, the aircrew was making a no-flap landing. After completing the landing checklist down to the landing gear, power was reduced causing the landing gear audible warning to sound. The horn silence switch was depressed and the approach was continued. Due to the low power that was required for the no-flap approach, the throttle was never advanced sufficiently to reset the warning horn. Subsequently, the aircraft was landed with the gear retracted. After sliding to a stop, a small electrical fire erupted in the belly of the aircraft, but airport personnel quickly extinguished it. The pilot being checked said he was distracted by a conversation concerning engine fire procedures. Also, he thought the check pilot had called that the landing check was complete. The check pilot stated that he had called only the no-flap checklist complete with the before landing checklist complete down to the landing gear. The proficiency flight was begun on a short notice when another check pilot could not be found.