Local and weighted transient temperatures in a cylindrical, cladded fuel rod and a single-phase compressible coolant are determined by a linear analytical model applying Laplace transformation. All independent variables determining the channel temperatures and the interaction between fuel, canning, and coolant temperatures are taken into account. Assuming constant material properties in the fuel rod, the calculation of fuel and clad temperature is shown to require four functions defined such that one argument is real and depends on geometry only. Material properties affect only the other (imaginary) argument, and different properties result in parallel displacement of the functions. These features enable a relative general presentation of the functions for various geometries and material properties. The functions determining coolant temperature may be given in an integral-free form if, essentially, the can-to-coolant heat transfer coefficient is space independent. The model was originally developed for use in steam cooled fast reactor analysis. It may be applied to other fast or thermal systems with single-phase coolants. Furthermore, it may serve as a means for evaluating numerical approximations of nonanalytical finite difference methods (e.g., to establish the necessary number of subregions).