I found this bug not so long ago, my character missed the Pyrobla... i mean, Pyrokinesis, and i got hit with it. So i started burning. I thought, the Exothermic Aura clearly says "Makes you immune to heat damage... et cetera". So i used it, but the status "Burning" still not disappeared. As i was wearing Rathound Regalia, it got me killed really quick. The saddest thing is, it was the last enemy out of, like, 10 people (Lurkers' base). So, yeah, my arse sure suffered some heat damage.
Long story short - the Exothermic Aura protects you from new "Burning" debuffs, but doesn't remove the existent ones. Which results in receiving Heat damage even while it says, that Exothermic Aura makes you Immune to it.
