NYC84FA059

During takeoff roll the overhead courtsey light flickered. As the acft lifted off the right front cabin door opened & the light remained on. The plt advised the tower he would be returning to land & entered a right downwind leg for rwy 27AT 500 ft AGL. The plt stated the interior of the acft became very noisy & cold so he elected to fly the downwind leg atabout 500 AGL to reduce the time of exposure to the elements. The ability to see the arpt was reduced on the right base as the plt had to look directly into the white overhead courtesy light. When the plt was able to see the arpt he was notin a position for a normal landing so he initiated a left turn to intercept the rwy 27 final approach path. The acft lost altitude rapidly & the tower issued two altitude warnings prior to the acft striking trees. The acft was destroyed by fire.