What would happen if an LED was run in a 500F/260C environment?
Packaging of most LEDs would degrade very quickly- epoxy breaks down at high temperatures, and I imagine the soft material used in some white LEDs (silicone?) would also degrade. 

Certain LEDs are made to withstand high temperatures and would probably last quite a while at that temperature (hours, perhaps) before degrading too much if the self-heating is kept to a minimum or they are not powered. I'm talking about expensive hermetic LEDs with glass or quartz windows, not your garden-variety cheap LED. 

The 260°C temperature may be briefly seen during IR reflow soldering of normal LEDs but the exposure is measured in seconds.

Speaking of which, you'd have to figure out how to attach to the leads (welding, perhaps) since ordinary solder would be molten. 

In operation, the wavelength emitted by the LED would increase substantially.. blue would tend towards green or yellow, and red would slip towards infrared, and there would be a commensurate decrease in forward voltage at a given current.