What would happen if most the fat in your body was rapidly converted into energy in 2 minutes?
It depends, but you're going to die.

Specifically, it depends on how fat you are. Even Andreas Munzer is going to die. At only 3% body fat, burning all his fat (9kcal/g) would "only" increase his internal body temperature by 270 degrees C. Factoring in the energy required to boil off his body moisture and adding in body heat leaves Andreas at  ~200 C or so (pretty unevenly distributed) minus whatever heat he could give off through his skin in two minutes. He's definitely dead, but probably not on fire. The flash point of animal fat oil is about 300 C, so most of his body probably isn't going to be hot enough to burn on its own. There will probably be some smoking, though.

The average body fat percentage is more like 22%(for males), and the numbers there are unequivocal. That person is going to catch on fire, as their body temperature is going to go up about ~1800 C after boiling off all the water. That's enough to melt your titanium hip implants. 

In short: you'll die pretty quickly, and then you might catch on fire before your two minutes are up, unless you're Andreas Munzer or another professional bodybuilder.