Thermal dissipation is like most other bionics - its effect stops at your skin, so your clothing can and will burn while you're under its effect. Try wearing some firefighter turnout gear and/or nomex clothing and/or survivor fire armor. And remember if the fire is sufficiently intense even combining thermal protection CBMs and fire protectant gear won't keep you going forever, so stay out of the really intense flames even if you have the proper gear.
I've not yet unlocked survivor fire armor then, although I did just realize that you can get chunks of Nomex from cutting up fire gear. Although looking through the json, it appears there's only the suit, no helmet, gloves, etc. for fireproof survivor gear. And I can't seem to find any flags that make it appear particularly fireproof either, except for having nomex as a material.
According to the wiki, you only become 'on fire' if standing in a maximum intensity fire, and even then the Thermal Dissipation CBM will prevent you becoming 'on fire'. While you are 'on fire' clothing you're wearing will take damage, though metal clothing will at a highly reduced rate (2% chance of damage per turn). So either you're mistaken about clothing, the wiki is outdated as usual, or I need to go walking through some fires.
ALSO: I had a dream in ASCII last night. I was in Cataclysm, wading through zombies in heavy armor, until I got hit by a giant white worm, which hit me hard enough to send me flying. And not just flying, but old school DF "goblin golf" flying, where I simply traveled in a straight line directly east, over a significant field and roads until hitting a building and dying instantly.
-I now suggest to include "Giant White Worm" as the 'hulk equivalent of worms'.
EDIT: I copied my save folder, lit a building on fire, and when it started burning in earnest I stood outside a few tiles, and activated BOTH internal climate control AND thermal dissipation. They both consumed power, but even standing a few tiles outside the fire itself, I suffered extreme heat. I didn't seem to get blisters, but I became so hot that I began vomiting and died of dehydration. I'm not entirely sure these bionics actually do ANYTHING, since that's the same way I've died in previous games.