you need to insulate the burn tunnel and riser, hint - insulative materials are usually very light in weight.....do a search for papercrete/paperclay ceramics or insulative refractory....
From the picture i notice that you have a short exhaust? Notice that in a rocket mass heater a lot of the heat is taken out through a long exhaust tube, the barel is not all the heat transfer surface. For trying it, it is ok.