You put their names in the title. Fire can defeat the cold-powered villains and Ice the heat-powered ones.
Batman is top in both categories. My next choice for a detective would be Jo Mullein, since she’ll be the Infinite Frontier’s greatest detective by the era of DC: Future State. But I don’t know how often she’s on Earth. Then I realized a cheat code: They don’t both have to be geniuses. Commissioner Gordon has been able to fool Batman into thinking he doesn’t know his secret identity. The world’s greatest detective and the only person who can fool the world’s greatest detective are the perfect choices.
Well, the Shade’s powers are dependent on his confidence. Fortunately, Jessica Cruz is an expert at both light and finding alllllllllll the dangers. After she defeats the Shade, Kyle Rayner shines his multicolored light into a prism that has been enlarged by the Atom, bathing the Earth in light. Of course, there are no seasons or years anymore… Well, you can’t have anything.
Flash (Wally West). He has super-speed and is unmoored.
Martian Manhunter can shapeshift into a gorilla to defeat Grodd while simultaneously using his powers to protect others from his mind control. Vixen defeats Cheetah, Krypto defeats Killer Croc (no one said they had to be the same animal), Beast Boy defeats Man-Bat. Animal Man defeats Copperhead, Yolanda Montez defeats Mammoth, and B’wana Beast defeats Killer Shark. And yes, I may have looked at the DC Database article on the Red to find out about different animal superheroes… There was no rule saying I couldn’t!