In the design of a small molten salt power reactor, one of the important problems is the heat deposition in graphite moderators, which are irradiated with high energy gamma-ray and neutron flux. To remove the deposited heat adequately, fuel salt should be distributed appropriately in the reactor core. A numerical study was carried out in this paper, and the main concern was about the temperature distributions in the graphite moderator elements and the fuel salt. The velocity distribution of fuel salt in the reactor core was increased in proportion to the heat generation distribution which was given from the preceding neutronic design study. The heat conduction equation with appropriate boundary conditions was solved by finite element method to simulate heat transmission process in the graphite moderators. It was revealed that the maximum temperature of about 1,150 K appeared in the graphite element in the blanket. The maximum temperature gradient of about 4 K/mm appeared in the element in the inner core (core I ). It was also estimated that the velocity of fuel salt was about 1.0 m/s in the core I, and 0.1 m/s in the blanket. The thermal design study represented in this paper suggested that the heat deposition would not cause severe restrictions to construct and to run the small molten-salt power reactor.