Ducky said that he hadn't found a way to get the roughness noise to be used over the entire node system. I Think I have a way to accomplish that. At least it worked in this animation.
This is what I did:
This gave me a flawless loop, with a noise pattern that covers the entire grid for more variety.
This is how my material looks:
I use an empty to control the heat gradient. But that is just because I like to adjust it from outside the material.