In this thesis, we consider the steady Boltzmann equation with diffuse reflection boundary condition. We study the case of hard potential and the non-isothermal boundary. We prove the existence and the uniqueness of solution and their estimate in both L 2 and L ∞ space. In L 2 the Theorem, we provide a direct way to estimate the kernel of the linearized Boltzmann operator. In the L ∞ Theorem, we introduce the stochastic cycles and prove the estimate that is valid for both steady and dynamic cases. And we provide a iteration scheme for the non-isothermal boundary temperature to prove the existence result and the L ∞ estimate when the wall temperature do not oscillate too much.