Mesoscopic scale simulations on heat transport in porous structures are shown with the coupled structure generation and transport simulation methods based on probability distribution functions in Gaussian quadrature grid and velocity sets (GQGVS). The mesoscopic scale method for various structure generation named a controllable structure generation scheme (CSGS) may generate not only multiple-phase isotropic homogenous random structures, but also shape-constrained anisotropic heterogeneous structures through relatively simple constraint integer indices with a high accuracy of global phase volume fractions. A nondimensional lattice Boltzmann method (NDLBM)-based solver for coupled transport equations is applied for direct mesoscopic scale simulations of thermal diffusion and natural convection in generated structures described by the local phase volume fraction matrix. Variable timesteps with transient mesoscopic March numbers and stretched space steps with local coordinate transformation gradients are discussed. The effective parallel NDLBM scheme with minimum information transferred during the data communication between subdomains is introduced. Two- and three-dimensional thermal diffusion and natural convection through various porous structures including random, sphere, fiber, and porous pellet packed structures are illustrated to provide a better mesoscopic scale understanding of the mechanism of heat transport in complex structures.