Is that heat in general or just heat caused by charging? In other words, can gaming, which tends to generate more heat, shorten the lifespan of your battery?
It does. And the battery in the iPad 3 / 4 already gives much more power than in the iPad 2 (and, probably, the iPad mini). This may be the reason for my iPad 2 (purchased exactly 18 months ago) has definitely less than twice the cycle count of my iPad 3 (purchased exactly 7 months ago - that is, less than half of that of the iPad 2): 241 vs. 140. (The usage patterns of the two iPads have been the same: I, and later, when the iPad 2 was handed down to her, my wife have used several hours a day both tablets.)
BTW, I've found a more quantitive ratio between charge rate (see the 5W vs. 12W question) and battery life: see "Figure 1: Cycle performance of Li-ion with 1C, 2C and 3C charge and discharge" at
http://batteryuniversity.com/learn/article/ultra_fast_chargers . That is, the Apple Store folks' statement (
"it will damage the longevity of the battery.") is certainly true.
However, this still doesn't mean the iPad mini's battery will surely die in, say, half a year or will burn if you always charge it with a 12W charger. I'd say its life expectancy will "only" be shortened from, say, 3 years to, say, 1.5.
Basically, I don't think you need to be afraid of explosions.