In hypersonic boundary layers, Mack mode is the most unstable mode and its secondary instability is a hot research topic on the laminar-turbulent transition. Understanding the mechanism of a secondary instability is very important to delay/promote turbulence generation. In this paper, we focus on the main routes of secondary instability to turbulence in hypersonic flows, including fundamental breakdown and subharmonic breakdown, especially the former one. Through the linear and non-linear stability analyse and secondary instability analysis at various flow temperature conditions, we are trying to find out the temperature effect on the secondary instability mechanism of Mack mode disturbances. The results point out that the fundamental mode always dominates the breakdown type when the saturated amplitude of the primary Mack mode is large enough. As the stagnation temperature increases, the maximum growth-rates of the fundamental mode and subharmonic mode both increase. Meanwhile, when the wall is cooling, the maximum growth-rates of the fundamental mode and subharmonic mode are both enlarged. In contrast, with the heating wall, the maximum growth-rates of the secondary instability both decrease.