Most players do not embrace the idea of jungling on Rumble seeing as how he excels at early-game laneing phase, however he serves as an even better ganker than he is a laner. If you need to fill a jungling role on your team, or simply enjoy ganking like a boss, then I recommend jungling on Rumble. Please read before voting (however I really cannot enforce that now can I?)

For marks I use Marks of Insight X9, standard for most AP champions.
For seals I use Seal of Fortitude X4 and Seal of Vitality Greater Seal of VitalityX5, this provides both early-game jungling survivability and late game health, I find it a good balance.
For glyphs, I use Glyph of Potency X4 and Glyph of Force X5, this gives me enough AP to clear the jungle early but still carry well.
For Quintessences I use Quintessence of Potency X3, great for early game jungling, with all of these runes you have 20 AP base to start out, before turning on your elixer.

For my masteries I go 10/10/10, going up to the jungling talents in all three trees. It would be very possible to substitute the utility tree for finishing the defense tree, but I prefer the extra experience and buff duration, this is determined by personal preference.

Jungling on Rumble sounds difficult, but ends up being incredibly easy.

I start with Elixir of Brilliance and HP pots X6. I start at golems, make sure that directly before the fight begins you have 80 heat or more and that your Elixir is on. Turn towards the golems and hit both of them with your flamethrower . This will overheat you, smite the one you want to kill and end it within moments. The other one will follow shortly. Make sure to be rolling health potions the entire time.
I then move to wraiths, you will have your scrap shield at this point. Enter this fight at between 60-75 heat. Turn on your shield , then overheat with flamespitter to kill the large wraith, the rest will follow. Continue to use your health potions throughout the entirety of the first phase of jungling.
I then move to wolves, they are so remedially easy that you should gain health during the fight.
I finish the first sequence at blue, at this point I have rank 2 flamespitter . I smite blue and demolish it. You will finish this fight with a small amount of health, but if you have enough you can gank bottom or middle right away. If not, recall and buy your first amplifying tome then commence with the demolition of the jungle, or begin ganking. When he hits level four and gets his harpoon he becomes and amazing ganker.
After a few ganks, or continued farming of the jungle, you will get your revolver , at this point you will be able to get red buff, making your overheat even more powerful.

For items, you must begin with junling elixir and potions , followed by a revolver . After this I get boots, I use boots of swiftness but given that Rumble is prone to being focused, I would pick up merc's treads if the opposing team has multiple stuns or disables. Following this I get crystal scepter , which is for all intents and purposes Rumble's core item. I follow this up with lich bane as this will add another element of burst and make your first hit of overheat unbelievably hard. My next item depends on the opponents' team comp, if they are ad heavy, I pick up the hourglass , if they are ap heavy or magic resist heavy I pick up abyssal scepter . I then pick up a deathcap . The order of the defensive item and the deathcap can be reversed depending upon whether or not you need more survivability or more damage at that stage in the game, you make the call. I finish by turning my revolver into will of the ancients unless someone on my team already has it, in which case I will make it into a gunblade . This is mainly for the slowing effect.

Ganking is very important on rumble because he can begin so early, sometimes as early as level 3 if you are ganking a lane with disable. If not, by level 4 your ganking can be exacted to a science.
Start the fight at 50-55 heat. Open with a harpoon on your target, the use scrap shield as you run towards the target and use flamespitter to overheat yourself . These should all be in quick conjunction such that your second harpoon is ready to either hit a second target or double stack your slow. With ghost on you can happily torch and auto-attack the enemy to decimate them thoroughly.

Remember that this is a relatively squishy build, but stacking ap will make your shield very strong, use it as such. Try to enter fights late as you are prone to being focused. Rumble shines early game, you should have several kills before level 9. Enjoy your delightful cliché, RUMBLE IN THE JUNGLE.