the closer the billy can to the flames, the faster it will heat up - remember inverse square rule - doubling the distance from the source results in one quarter the heat!
the wider the diameter of the pot, the faster it will heat up as surface area to volume is a factor
the blacker the pot, the more heat it absorbs and the faster will be the heating - hence cast iron beats stainless steel for larger cooking needs such as baking, roasts but the much heavier weight means the pot itself takes longer to heat up (and much longer to cool down)