In the present work the dependence of the heat transfer coefficient between Cu and Sn, Cu and Pb, and Cu and W on the temperature and an external magnetic lieM has been measured. The preparation of the metal-metal junctions has been performed by melting so that a close contact at the interface was guaranteed. The heat transfer coefficient has been found by a steady-state measuring method. In the case of the Cu-Pb junction the heat transfer coefficient could be measured both in the superconducting and normal states. For all the metal-metal junctions in the normal state a linear temperature dependence of the heat transfer coefficients on the temperature has been found. In the superconducting state a strong reduction of the heat transfer coefficient has been observed. In addition, a theoretical calculation of the heat transfer coefficient on metal-metal interfaces is given. First we consider the scattering of electrons on a steplike potential barrier between two gases of free electrons. Then the thermal conductance due to scattering in an alloy layer is calculated. Such an alloy layer may arise from diffusion during the contact preparation. Comparison of these two cases with the experiments shows the thermal conductance at the interface is mainly determined by the electron scattering on lattice irregularities in the diffusion layer.