A microscopic thermal model for dry sliding contact that accounts for a volume generation of the friction heat is proposed. A numerical procedure that allows the determination of the two parameters alpha and R(sl) of macroscopic thermal models for dry sliding contact is given. The results are compared in the case of a simple contact geometry, with an analytical solution for alpha and R(sl). The influences of the microscopic parameters, the contact geometry and the velocity on the two macroscopic parameters are shown.