Filling of an empty cryogenic vessel initially at atmospheric temperature with a cryogenic liquid at its saturation temperature will initiate a high temperature difference between the terminals of the annular space containing the thermal insulating material. This high temperature difference is behind the dependence of thermal properties of the thermal insulation material on its temperature. Based on the authors¿ own research and classroom experience, this book contains two parts, in Part (I): the 1D cylindrical coordinates, non-linear partial differential equation of transient heat conduction through a temperature dependent thermal conductivity of a thermal insulation material is solved analytically using Kirchhoff¿s transformation. In Part (II): the 2D body-fitted coordinates, non-linear partial differential equation of transient heat conduction through a temperature dependent thermal properties of a thermal insulation material that is subjected to a natural convection heat transfer boundary condition associated with a periodic change in ambient temperature and heat flux of solar radiation is simulated numerically using the fully implicit Finite Volume Method