Because I was asked, here's a live demo that works in your browser :D
madeio.net/flame/

But wouldn't I have to do this analytical calculation and therefore texture mapping per fragment? Sounds pretty expensive

simonschreibt.de/gat/stylized...
The first video, the first part of the video. But in general I really recommend his blog, learned a lot.

But I also used some force fields, as described here
sighack.com/post/getting...

Thank you so much. I've always wanted to try ray marching, but reflections seemed a bit boring. I'll definitely look into it.

Do you have resources explaining what you are using raymarching for? I only know the technique from reflection mapping.