Heatproof would conflict with Dry Skin in terms of flavour and effect. Weirdly enough, this Fire-type isn't fond of others' flames.
To be honest, I wasn't expecting someone to take this seriously.
As far as flavor, I already mentioned how the shell acts as an insulator. I think that
Dry Skin refers to the body of CAP3 (despite the art of him opening up the cap on his lamp to absorb water), while
Heatproof refers to how lava lamps have thick glass to resist cracking, or insulation, or something like that.
As far as effect, there are a couple instances of Pokemon having conflicting abilities. Two poor examples that I can think of right now are Spinda's Own Tempo and Tangled Feet (immune vs. benefit) and Zangoose's Immunity and Toxic Boost (also immune vs. benefit). At this point, I like the idea of Heatproof, so I would appreciate discussion by anyone who agrees with me.
tea_and_blues also mentioned
Damp, which I support because it goes with Dry Skin (like the Paras evolutionary line) and it's literally useless in OU.
kjt mentioned something interesting about
Magic Bounce. Though I vehemently disagree with giving CAP3 something as good as Magic Bounce, it made me think; CAP3 can use both Toxic and Will-O-Wisp without fear of them being reflected as it is immune to both the statuses it can, by nature, inflict. This could be useless as the two Magic Bouncers carry a supereffective STAB or it could be an interesting dual-status inflicting niche.