The only proper way to do this is game by game:
MM1: Too close to call between Iceman and Fireman.
MM2: Heatman's theme is one of the lesser tracks of the game. So whether you consider Bubblean or Freezeman (or even Airman) to play the "cold" role, cold wins.
MM3: Geminiman > Shadowman. So cold wins.
MM4: Too close to call between Dustman and Cossack Stages 1-2
MM5: Waveman > Chargeman. Cold is up 3-0 now.
MM6: Blizzardman > Flameman. 4-0 cold.
MM7: No clear winner between Turboman and Freezeman.
MM8: Swordman > Frostman. Hey, hot's on the board!
MM&B: No clear winner between Coldman and Burnerman
MM9: Magma Burning > Splash Blue. Cold's lead is cut to 4-2.
Classic score: 4-2 cold.
X1: Flame Mammoth > Chill Penguin. Hot.
X2: Flame Stag > Bubble Crab. Hot.
X3: Tough to call since Vile's stage is really the only thing here that can represent "hot".. but it's better than Blizzard Buffalo's theme, so hot it is.
X4: Tempting to give to Frost Walrus since he has two themes, but Magma Dragoon's gonna eek this one out.
X5: Has to go to Burn Dinorex since Tidal Whale must be disqualified for reusing music from an earlier game. >_>
X6: No brainer here. Blaze Heatnix is the obvious winner.
X7: Too close to call between Naval Battle and Burning Water.
X8: Avalanche Yeti > Burn Rooster. Shutout averted!
X score: 6-1 hot.
Z1: Can't make a ruling on Scorching Desert vs Infiltration.
Z2, part 1: Gravity > Ice Brain. Hot.
Z2, part 2: Passionate > Cool Water. Hot.
Z3: Trail on Powdery Snow > Volcano. Cold.
Z4: Max Heat > Sleeping Beast. Hot.
Zero score: 3-1 hot.
ZX, part 1: Wonder Panorama > Ogre Claw. Cold.
ZX, part 2: Ultramarine Meditiation > High-Press Energy. Cold.
ZXA, part 1: Target Chaser > Drifting Floe. Hot.
ZXA, part 2: Overloaded > Flashover. Cold.
ZXA, part 3: Brimstone > Organic Line. Hot.
ZX score: 3-2 cold.
MMNT: Net on Fire > Waterworks. By a long shot. Hot.
BN1: Too close to call between the oven and the waterworks.
BN2: No cold stage, no contest.
BN3: No hot or cold stage.
BN4: No hot or cold stage.
BN5: No hot stage.
BN6: Robo Control PC > Aquarium. Hot.
SF1: No cold stage.
SF2: No hot stage.
SF3: Somebody rip the music from this game already so I can judge it!
BN/SF score: 2-0 hot.
Net result: 3 series to hot, 2 to cold.
15 games to hot, 9 games to cold, 7 ties, 6 insufficient competition, 1 music unavailable.
Poll