Mobafire's stat system is messed up. These are the actual in-game stats:
http://leaguecraft.com/builder/rumble/?items=108,38,55,22,84,117&runes=11,11,11,11,11,11,11,11,11,63,63,63,63,63,63,63,63,63,52,52,52,52,52,52,52,52,52,34,34,34&level=18&masteries=0040040001000000003304301000033010000000000000000

Here's the math. I compared my build with a standard tanky AP build consisting of Rabadon's, Rylai's, WotA, Abyssal Scepter, and Guardian Angel with CDR boots and this is what I found.

The combos I tested take into account autoattacks over the course of a 6-second overheat caused by Flamespitter and the autoattacks landed over the roughly 4.5 seconds it takes to initiate Overheat with two Flamethrowers, two Scrap Shields, and both activations of Electro Harpoon.
The damage range I added to the estimate with Madred's was figured from a minimum of 2k HP and a maximum of 4.5K HP.

Hybrid Rumble Build
-Overheat combo
1070 physical from autoattacks
1460 magic damage from Junkyard Titan
18.8% of hp magic damage from Bloodrazors
1057 from flamethrower
3587+30.6% of HP in one overheat
4200-4970 total damage

-Standard combo
Q-813
W
E-310
W
Q-1057 (Danger Zone)
2180 damage from spells
1164 physical damage from autoattacks
+23% of hp magic damage from Bloodrazors
3344+23% total damage
3804-4400 total damage

Standard Rumble Build
-Standard combo
Q-1104
W
E-836
W
Q-1435 (Danger Zone)
3352 damage from spells
432 damage from autoattacks
3784 total damage

-Overheat combo
576 physical damage from autoattacks
1304 magic damage from Junkyard Titan
1435 from flamethrower
3315 total damage

I actually forgot to take the extra AP from Rageblade's passive into account, which would edge the advantage further in my build's favor. Regardless, my build does more damage and has more sustainability due to making full use of Hextech Gunblade. Rumble remains very tanky with the same HP and just slightly less resistances, but with higher HP gain due to the combined lifesteal and spell vamp. The spell pen I build from Abyssal and my rune/mastery setup also synergizes well with Madred's and Overheat.

The goal with this build is not to skirt Overheat by staying in the Danger Zone with carefully timed spells, but to push yourself into Overheat as fast as possible and completely shred the opponent in the process. AP Rumble has to carefully manage his spell activation and can't spam all the time for fear of Overheat, but hybrid Rumble uses Flamespitter every chance he gets and shines the most when pushed into Overheat. The other benefit of this is that you can rush in and Overheat right at the start of a fight and you'll have an empty heat bar by the time things start to go bad if that happens at all.

When the match begins you should call solo top and start with Flamethrower regardless of the map you're on (except Dominion, of course. I'll add a Dominion section as I update.) Get W second and E last, maxing R>Q>W>E. Harass by popping your Scrap Shield and Flamethrower at the same time while running at an enemy when they get close. Most foes will see how much damage they're taking and run; if they continue to attack back off and nail them with both shots of E. Wait until your heat bar drops low enough that W can be activated to push you barely into the Danger Zone and Q again for tons of damage. Rinse and repeat until they die or you get your ult, then wait until they're low and try to ult when they engage you up close so they have to stand in the DoT a long time.
In teamfights, try to land your ult on as many of the enemy team as possible and W-Q rush in on the easiest enemy to kill. Try to make sure you have enough heat to pop Scrap Shield and run if things get hairy.

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