An optimal control problem, concerned with a heat conduction process of a moving material in a furnace, is posed. Due to the stochastic nature of the process only a suboptimal version of the problem is treated. This is done in the following manner. First the process is modelled by using an adequate stochastic partial differential equation. Then, sufficient conditions are found on suboptimal controls in the form of a sot of non-linear partial differential equations. Finally, a central finite differences scheme is proposed to solve the set of equations, and the applicability of the scheme is demonstrated by examples.