Five different methods for determining optimum fluid temperature changes during heating or cooling thick plate are examined. The first method presented in this paper is based on the discrete form of Duhamel's integral. The method can be easily applied to bodies of complex shapes and is recommended for use, while three other methods: the Laplace transform, Burggraf analytical method, and space marching method can be applied to only a very limited number of optimum control problems. In the fifth approach, the optimum fluid temperature changes are approximated by a function with unknown parameters, which are determined using the least squares method. These five techniques were used to determine time changes of fluid temperature assuring linear increase of the slab wall temperature at the given location inside the body. No one approach is perfect. The optimum fluid temperature changes are burdened with a large uncertainty at the beginning of the heating process. (C) 2008 Elsevier Ltd. All rights reserved.