The hot blast stove is an important facility in the steel industry, which of the expansion gaps design has a significant buffering effect on the thermal stress with a high-temperature operating process. In this paper, a 3D numerical model of a hot blast stove was established to calculate the thermal stress distribution and analyze the remaining thickness of expansion gaps with different parts during the operating process. Young’s Modulus of the refractory linings was obtained by comparing with the experiment data and numerical data under the different temperatures and considering the influence of mortar. The result shows that Young’s Modulus of the refractory brick increased as the temperature, and the comparison of the experiment and simulation data of Young’s Modulus under three different temperatures displayed good agreement between the two sets of data. The first/third principle stress for the refractory linings can be reduced effectively by designing the expansion gap rationally, and the equivalent stresses of the shell are mainly concentrated at the joint and the neck. In addition, the expansion gaps are decreased under the thermal expansion and moved along a radial direction for the combustion/checker dome and the combustion/checker chamber.