In the present work, molecular dynamics (MD) simulations have been performed to study thermal properties of crystals in a one component soft-core system. The system was examined along the phase-diagram using the compressibility factor, (T*) ≡ PV/Nk_BT plotted against the reduced density ρ* (or reduced temperature, T*). The specific heat, C_V, of the system is presented as the function of (ρ*) and also as the function of the reduced potential energy, U*. These C_V values are expressed using coefficients of the expansion around the harmonic term. We also derived the expression for entropy using these coefficients. The contribution of an anharmonic term in the specific heat and entropy was clarified by this. These results are compared with those obtained from the fluctuation of kinetic energy. Several quantities related to the distribution of time dependent reduced temperature and dynamical compressibility factor (PV/Nk_BT)_t are also examined and three T* regions of thermal behaviors are characterized. In the diagram, the glass transition by cooling or compression can be treated on the same basis. Results of the present work will be helpful for a better understanding of the changes in the specific heat during the glass transition in the future works.