The thermal characteristics of solid nitrogen are investigated by experiment and analysis for the purpose of evaluating its feasibility as a cooling medium for HTS (high T$_{c}$ superconductor) magnets. A cryostat to refrigerate a liquid-nitrogen container well below its freezing temperature with a 2-stage GM cryocooler is designed and constructed. The spatial distribution of temperature is measure as a function of time during the freezing and melting processes. from which the thermal diffusivity of solid nitrogen can be approximately calculated. the freezing process is formulated and solved by the integral method with an assumption of phase equilibrium at the solid-liquid interface and experimental observation. It may be concluded that the thermal diffusion in solid phase is much slower than in liquid and the degree of super-saturation is quite severe in the solidification of nitrogen.n.