The solution of the mixed quasi-stationary heat conduction problem for the ring has been obtained by using a finite Fourier transformation. The heating on the external side surface of the ring due to any locally distributed heat flux, as well as the convective cooling from internal side surface and from the end faces are considered. It has been proved that for some special geometrical and thermo-physical parameters of problem the received solution agrees with well known studies. The influence of some distribution intensity form of heat flux on the maximum temperature was studied.