The work described in this technical report was undertaken as part of a larger program dealing with a systematic investigation of changes in the physical prosperities of artificial graphite due to neutron bombardment. Very pronounced among those changes is the increase in the elastic modulus. Since there is a general relationship between the elastic modulus of a given substance and its specific heat, it was expected that corresponding changes will occur in the specific heat. In conclusion, the experiments determined that it appears that the low temperature specific heat measurements of strongly bombarded samples will be helpful for the understanding of the nature and the mechanism of the changes produced by neutron bombardment and annealing.