Except that leather caps aren't much use in combat, which the original scenario was about.
Well dragon breath attacks are far more like a flamethrower, which kinda breaks the thermal energy transfer numbers I crunched which are intended for a split second duration spell.
You're also far more likely to die before you get to the 40.4kJ energy required to achieve a fourth degree burns to ~18% of the body (first degree burns to the same area only needs about 3.6kJ if my math is right).
As for protection, helms give a surprising amount assuming you can keep the gaps out of the direct stream - I remember one full contact re-enactor saying that the only safety requirement was that a 1/2" steel rod can't get into any of the eye/air slits.
As an aside, fat melts at about 184C, so you're likely to be dead well before then.
What are you doing as a paramedic all the way over there, if you don't mind my asking?