In this article, the object of the study is focused on the influence of local insulating materials in the design of a calorific model for the conservation of hot water for a fixed period. The short hollow cylinder is wound with thermal insulation flax between the two walls of the cylindrical device to insulate the interior temperature. The objective of this study is to see the behavior of the thermal resistance of the material as a function of the insulation thickness. The cylinder is modeled by applying the transient analytical method with the heat equation. This analytical resolution of the thermal equation makes it possible to determine the detailed expression of the thermal resistance but also to visualize the evolution curves of this resistance according to the thickness of the insulation under the influence of the contact resistance thermal and heat exchange coefficient on the outside cylinder wall. The results obtained show that the optimum insulation thickness of linen at a temperature of 90 °C is 3.7 cm under the influence of the thermal resistance of the material and 4 cm under the influence of the exchange coefficients thermal.