In this paper, a corrected smoothed particle hydrodynamics (SPH) method is proposed to solve the problems of non-isothermal non-Newtonian viscous fluid. The proposed particle method is based on the corrected kernel derivative scheme under no kernel derivative and incompressible conditions, which possesses higher accuracy and better stability than the traditional SPH method. Meanwhile, a temperature-discretization scheme is deduced by the concept of SPH method for the purpose of precisely describing the evolutionary process of the temperature field. Reliability of the corrected SPH method for simulating the non-Newtonian viscous fluid flow is demonstrated by simulating the isothermal Poiseuille flow and the jet fluid of filling process; and the validity and accuracy of the proposed SPH discrete scheme in a temperature model for solving the non-isothermal fluid flow are tested by solving the non-isothermal Couette flow and 4:1 contraction flow. Subsequently, the proposed corrected SPH method combined with the SPH temperature-discretization scheme is tentatively extended to include the simulation of the non-isothermal non-Newtonian viscous free-surface flows in the ring-shaped and C-shaped cavities. Especially, the convergence of numerical simulations is analyzed, and the influences of heat flow parameters on the temperature and fluid flow at different positions are discussed.