THE FLT WAS IN CRUISE AT FL 350 WHEN THE CABIN CREW REPORTED A CABIN FIRE IN THE VICINITY OF SEAT 28A. SHORTLY AFTER, A LOWER AFT BODY OVERHEAT WARNING WAS RECVD. THE FLT DIVERTED TO RICHMOND, VA. DURING DESCENT, THE FLT CREW PERFORMED THE APPROPRIATE CHECKLIST AND THE LOWER AFT BODY CVHT LIGHT WENT OUT ABOUT 3 TO 4 MINS. AFTER IT ILLUMINATED. LATER EXAMINATION REVEALED THAT A PAX HANDBAG THAT WAS ON THE FLOOR AGAINST THE CABIN EXHAUST OUTLET ADJACENT TO SEAT 28A WAS EXTENSIVELY FIRE DAMAGED. THE CARPET UNDER THE HANDBAG WAS UNBURNED EXCEPT FOR A SMALL PORTION LEADING TO THE CABIN AIR EXHAUST OUTLET. LOCALIZED FIRE DAMAGE WAS PRESENT BEHIND AND BELOW THE OUTLET. AMONG THE CONTENTS OF THE HANDBAG WAS A BOTTLE OF HAIRSPRAY, FOUND WITH THE CAP LOOSE. THE LABEL ON THE BOTTLE WARNED THAT THE CONTENTS WERE FLAMMABLE. ROW 28 WAS IN THE SMOKING SECTION FOR THAT FLT.