A numerical method of a lattice kinetic scheme based on the lattice Boltzmann method for incompressible viscous flows with heat transfer, which was proposed by Inamuro [Phil. Trans. R. Soc. Lond. A 360 (2002), 477-484], is developed and applied to thermal fluid flow problems through a porous structure. Flow characteristics and temperature profiles at a pore scale in the structure are obtained at Reynolds numbers up to where Re is defined by using the superficial velocity and the equivalent diameter of the bodies. Calculated pressure drops through the structure are compared in good agreement with the empirical equations based on experimental data. In addition, for the time-dependent flows, velocity fluctuations and their power spectra are examined at different points in the structure. The present simulations indicate that the method is useful for the microscopic investigation of turbulent flows with heat transfer through porous structures.