Copyright © 2016 CC-BY-3.0 and by the respective authors. The amount of the heat generation in the beam dump for unstripped H- beam at an injection in a high power beam synchrotron becomes a few thousand watts. In such case, the temperature of the dump materials might reach unacceptable values from the aspect of the mechanical strength decrease. The thermal analysis for the injection beam dump at J-PARC 3GeV synchrotron was performed in order to evaluate the upper limit of the beam power into the dump. The temperature distribution of beam dump was calculated by modelling the detail configuration and enough large region. The upper limit of the beam power into the dump, which keep the concrete temperature below permissible value, was estimated to be about 3 kW. The comparison with the measured temperature shows the thermal resistance between the contacted materials should be considered for more accurate calculation.