The warming you are speaking of is the result of residue (combustible carbon products, tobacco oils, etc.) in the bottom of the bowl completing the combustion cycle . As pointed out in earlier posts, this is the result of the drastic increase in oxygen at the bottom of the bowl. When you dump the ash and dottle, you are leaving a fine layer of material, that is currently undergoing the combustion process, deposited on the interior of the bowl. The increase in oxygen suddenly and rappidly accelerates the combustion process, thus resulting in the warming sensation you are noticing. I suspect the reason you notice this more in the briars than other pipes is that briar wood tends to have higer specific heat (meaning that more heat is required for the wood to transfer heat and that the wood hold that heat longer. The heating process can be viewed by the following Q=m*c*dt (keep in mind this is a vastly simplified version of the equeation). Where Q is the rate of energy release (or heat transfer rate), m is the mass of the of pipe, c is the specific heat of the wood, and dt is the change in temperature with respect to time. Since the amount of heat produced due to the combustion of the residue left in the bowl is significantly higher than the temperature of the bowl, the heat transfer is faster allowing you to notice the warming sensation. Conversly, with other wood the lower specific heat results in an overall faster heat transfer and cooling resulting in a quicker and more complete combustion of the residue prior to dumping your ash and dottle.
