What was found
DURING DESCENT FROM FL380 TO FL 330 THE DUCT OVERHEAT LIGHT ILLUMINATED AND A VERY STRONG BURNING SMELL ENTERED THE CABIN AND COCKPIT. THE DIFFICULTY IN BREATHING CAUSED CREW TO SUSPECT POSSIBLE SMOKE SO THEY DESCENDED QUICKLY AND DECLARED AN EMERGENCY, REQUESTING A LANDING CLEARANCE AT NEAREST AIRPORT. THEY WERE DIVERTED WHERE THE AIRCRAFT HAD A NORMAL LANDING. INITIAL REVIEW BY LOCAL MAINTENANCE FOUND NO APPARENT CAUSE OF WARNING INDICATION AND SMELL SO THE AIRCRAFT WAS REPOSITIONED TO SERVICE CENTER FOR FURTHER TROUBLESHOOTING AND REPAIR.