Just chiming in here. I do not think burning the compost is going to speed things up. As Henderman has said, heat is generated because the bacteria and micro-organisms are doing their job. Heat is how you know they are working. Creating your own heat through burning will be counterproductive, as it will kill off all the good stuff that would otherwise be generating the heat.
My pile was not getting hot enough. The cause was not enough nitrogen. I went to starbucks and asked for a bag of their discarded coffee grounds. I mixed it in to my pile, and voila--within 3 days I went from 60 degrees to 115.
All that coffee causes high acidity though, and one thing you can do that is fire related is to add in wood ash. I just happen to heat my house with a wood burning stove, so I have plenty of that.
Anyway, good luck. Let us know how your compost journey is going.