Applying linearization and Laplace transformation the transient temperature distribution and weighted temperatures in fuel, canning and coolant are calculated analytically in two-dimensional cylindrical geometry for constant material properties in fuel and canning. The model to be presented includes previous models as special cases and has the following novel features: compressibility of the coolant is accounted for. The material properties of the coolant are variable. All quantities determining the temperature field are taken into account. It is shown that the solution for fuel and canning temperature may be given by the aid of 4 basic transfer functions depending on only two variables. These functions are calculated for all relevant rod geometries and material constants. The integrals involved in transfer functions determining coolant temperatures are solved for the most part generally by application of coordinate and Laplace transformation. The model was originally developed for use in steam cooled fast reactor analysis where the coolant temperature rise and compressibility are considerable. It may be applied to other fast or thermal systems after suitable simplifications.