Understanding Hagedorn Temperature: Can Light Speed Up?

[theLHC]

Hey guys, I was just wondering. If light can slow down at the temperature of 0 degrees Kelvin, isn't it possible for light to speed up if it was in a medium that had a temperature of 10^30 degrees Kelvin, which is roughly the highest temperature attainable in nature.

Your thoughts on this please.

 

[Vanadium 50]

The speed of light is the speed of light, I am afraid. Heating it doesn't make it faster.