Rumble'sultimate can deal a lot of damage if you stay inside the area of effect. When you see the missiles falling, move out of the way as quickly as possible.
Rumble deals almost entirely magic damage. Build some Maagic Resistance to reduce his damage.
It's important to keep a close eye on your Heat Gauge whenever casting, with the exception of The Equalizer. All of Rumble's abilities are stronger in the 50-99% Heat range, but overheating (100%) will silence you.
Spam Flamespitter at the beginning of the game to get in the danger zone, increasing your damage.
The bonus damage on Junkyard Titan can be just enough for the kill, but be careful, because if you were relying on one of his standard abilities to help you pick up the kill, the silence due to overheating can end up denying you a kill.
Consider leveling Scrap Shield for a low cooldown movement speed boost, and an effective clutch shield. You can also use it to always stay above 50% Heat.
The Equalizer receives no benefit from being cast above 50% Heat, so it can be wise to cast early so that you don't risk being overheated when you really need it.
Proper placement of The Equalizer can completely change a teamfight. Depending on where it is placed, Rumble can punish enemies attempting to enter a teamfight, damage most enemies already within the teamfight, or cut off the escape route of enemies wishing to exit the teamfight.
When casting The Equalizer, note that the point from which the cursor is dragged will become one end of the trail.
The Equalizer has a very large casting radius. Rumble can often surprise enemies by casting it from behind a wall.