The motions of the granular bed inside a rotary furnace are governed by complex dynamics consisting of two modes. The axial velocity of the active layer on top of the bed represents the fast mode, while the overall velocity in the bed follows a slower mode. The proposed nonlinear model focuses on the dynamics of the slow mode. The difficulties of an analytic solution are avoided by a numerical method that employs several correlations. The model can reproduce the experimental transient responses. It is concluded that rotary furnaces respond better to small amplitude excitations than to large ones; consequently, closed-loop control is well suited for this type of furnace.