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Here, we explore the sensitivity of the Casimir force between two topological insulator plates on thermal fluctuation using weak and strong magnetizations on the surface of plates via Lifshitz theory. Thermal fluctuations between two plates made of topological insulators in vacuum lead to attractive interactions. By considering a weak magnetization, the influence of thermal fluctuations becomes stronger compared to the magnetoelectric effect in the regime of large separations which leads to generating the strong attractive Casimir force. Moreover, by considering strong magnetizations it is observed that thermal effects cannot make a change in the attractive and repulsive Casimir forces, and magnetoelectric effect determines both the magnitude and direction of Casimir forces. In the range of small magnetization, thermal effects have a significant effect on the repulsive Casimir force. It has been shown that at high temperatures, repulsive interaction due to antiparallel magnetization becomes weak, so that they disappear by increasing the separation.