For the sake of the argument, let's say that the Fear Hax doesn't work.
Amaterasu has heat comparable to the sun, and Naruto blocks it with his globby Tailed Beast chakra. The same Tailed Beast Chakra is the same one Naruto used in say... Final Valley in part one. This aura, according to a google search, would be able five times hotter than the sun (Amaterasu), since it's comparable to lightning. Fair enough, but are we seriously going to say that a mastered Kurama Chakra Mode cloak is NOT five times more powerful than that primitive transformation from like a million episodes and chapters ago? Naruto should be tough enough to just... tank the heat.
Also, Sasuke's Jutsu Kirin utilizes natural lightning itself to attack- which would have that same amount of heat. Itachi with Susano'o can guard it just fine even without the Yata Mirror. Since Itachi and Naruto are comparable with Naruto using an unmastered KCM- Naruto should have the same heat resistance.