Analysis of tunnel kiln performance to determine the relation between input energy (Hf) and useful output energy (H,), by application of the integral energy equation, is shown to lead,to a firing equation of standard form. This is a concave-upward curve, from an idle firing rate (H-t(o)) at zero output to, theoretically, an infinite firing rate at a maximum output (H,m)., The corresponding curve for the thermal efficiency, eta = H-s/H-f, then also follows the standard form, being an asymmetric, inverted U-shape. The auxiliary expressions obtained for the constants in the firing equation: idle heat, maximum output, and intrinsic efficiency (alpha (o)(ro)), are then all shown to have significant dependence on the heat exchanger elements incorporated in the tunnel kiln design. Unusually, for the optimum design configuration at the theoretical adiabatic limit, the thermal efficiency for this system converges to 100%, and the processing efficiency can converge to infinity. These are limits that, are impossible to achieve in practical operations, but they provide a basis for evaluating expected design performance. The analytical structure is developed specifically for the tunnel kiln, represented as a firing section flanked by two (upstream and downstream) heat exchangers; but the general design and theoretical structure has potentially wider application, particularly with respect to the influence of heat exchangers in a furnace system where this has been given little earlier attention in the context of the furnace analysis protocol.