Part I of this series of papers (GARBAI-FENYES [15]) We have given the foundations of the system theoretical treatment of the heat flux based on the Laplace transformation method. Moreover, in the cases of the half space, the region bounded internally by the sphere, the sphere, the authors have proved criteria guaranteeing the existence of the convolutional representations of the heat flux depending on the known temperature. In Part Il (see [16]) the authors have solved the problem and proved the above criteria for the region bounded internally by the circular cylinder and the infinite circular cylinder. In this Part IU the authors have solved the problem and proved the above criteria for the finite rod and the region bounded by two concentric infinite circular cylinders.