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McDonalds recently started serving Rocky Mountain Oysters here in Montana---They call them (GROAN) McNuts. 
There is a lot of water in the body (~70%) and that would have to be 'boiled off' before the fire would be self-sustainable (just like a bonfire with green wood. There needs to be enough fuel on board to do this. Ignore the fact that there is a mixture of tissues and structures, each kg of body will contain 0.7kg of water. The energy needed to evaporate this would be about 1.6MJ. If you used fat as a fuel for this, with an energy content of about 4MJ per kg, you would need about 0.25kg and there's 0.3kg available.This is 'marginal' but worth following up. It implies that there is the right sort of amount of fuel available if everything is arranged right. You will have other heat losses and not all the non-water in the body is fat.
But, the 'spontaneity' issue - that is very unlikely - very few things burst into flames just like that.
But I'd have thought that much of the non-mineral, non-water component of the body is combustible (proteins and sugars should be able to burn just as well as fat).