The evaluation of thermal properties of actinide oxide fuels is a problem of high importance for the development of new generation reactors. In the present study, an expression obtained for n-dimensional Debye functions is used to derive a simple analytical expression for the specific heat capacity of nuclear fuels. To test the validity and reliability of this expression, the analytical expression is applied to $UO_2$, $NpO_2$, $ThO_2$, and $PuO_2$. It is seen that the formula was in agreement with the experimental and theoretical results reported in the literature.