Nemesis: Martian Manhunter
Other Major Foes: The JLA, The Army of the Endangered
Appearances: 15+ comics.
Powers: Fire projecting technology. As Inhuman Flame: Flight, strength, nigh-invulnerability and size alteration.
Bio: Mike Miller was a minor inventor/thief who had a brush with the greatness of Libra. This led him to alienate pretty much the entire metahuman community, until he was transformed into the monstrous "Inhuman Flame" and trapped in outer space by Green Lantern John Stewart.
Win: Effigy (8-4)
Lose: Human Squirrel (6-7); Scorch (4-9)
Nemesis: The Flash
Other Major Foes: Flash Rogues
Appearances: 200+ comics, plus roles in animation and video games
Powers: Fire generation.
Bio: In the Silver Age, Heat Wave was a themed robber whose rivalry with Captain Cold eventually turned toward their teaming against the Flash. Post-Crisis, he became a murderous serial arsonist pyromaniac.
These characters have remarkable similarities in powers, costumes, and perhaps most importantly, my general disinterest in either of them. Comic books are crawling with fire guys, in their respective circles each villain has a charisma deficiency, and both have been radically altered in recent years to try to drum up some kind of audience. In a fair match, I'd favor Heat Wave, if only for his sheer number of appearances and having given the Flash some trouble. Despite trafficking in the Martian Manhunter's specific weaknesses, the Human Flame never really put the Alien Atlas out. On the other hand, pre-Flashpoint, the Inhuman Flame reached grandiose levels of might that qualified him to take on whole teams, where New 52 Heat Wave fought Barry Allen like once and then ran right back to the Rogues.