A model able to describe the transient behaviour of a whole cylindrical feedstock heater is proposed. Besides the algebraic equations relevant to the radiative transfer, thermal balances are written for both the convection zone and the radiative one. The resulting system of Partial Differential Equations has been converted into an Ordinary Differential Equations one. Particular attention is paid to the way in which the equations are manipulated to make them as explicit as possible. However, because of the intrinsic stiff nature of the problem (too different characteristic times are involved) an implicit integration method must be used. Due to the algebraic constraints at the boundary of the refractory wall, the system to be solved consists of both Ordinary Differential and Algebraic Equations so requiring a careful computation of the initial conditions to allow the integration algorithm to start.