The paper presents a numerical solution of transient flow in superheaters in the state of parallel- and counter flow. The time and space temperature distributions of the working media and separating wall were evaluated. The partial differential equations describing the mentioned heat transfer were also solved using the method of lines coupled with Gear's method. Furthermore, the above temperature distributions were obtained by solving the mathematical model describing the conservation laws of mass, momentum and energy. Obtained results were compared to the suggested approximate solution.