I am not sure if u are referring to a malfunctiong LED or incandescent bulb. Considering the low quality of previous low beam optics in Chaiwanese headlights presented here earlier, I am not a bit surprised if LEDs are running at too high current at the temperature they were designed for. If the LEDs that were used had any datasheet for the manufacturer to follow.
How do you fix it... well you get some LEDs with a datasheet and run them at lower current which means you kind of have to do the design job the manufacturer was supposed to do in the first place. Very few LED factures have datasheet available, but if you buy recognized brands like HP, Lumiled, Nichia, Toshiba etc, datasheet is normally available.
Example of a LED datasheet from HP is:
http://www.farnell.com/datasheets/158.pdf
Especially Fig 4 (maximum forward current vs. Ambient temperature) is important for using LEDs in vehicles.