A new solid wedge thermal resistance model is developed in this investigation and used to solve the relation of the critical and the neutral thickness and heat transfer characteristics for an insulated regular cubic box based on its varying surface area. It is found that the dimensionless heat transfer characteristics of the insulated cubic box are the same as those of an insulated sphere. It is also found that the conventional constant surface area plate model cannot be used to analyse the insulated cubic box, especially at the situations of small to medium box sizes and or with a greater insulation thickness. The solid wedge thermal resistance model should also be applied to the heat transfer problem of the block having a shape similar to a solid wedge.