In this paper, an incompressible two-dimensional (2D) and three dimensional (3D) thermohydrodynamics for the lattice Boltzmann scheme are developed. The basic idea is to solve the velocity field and the temperature field using two different distribution functions. A derivation of the lattice Boltzmann scheme from the continuous Boltzmann equation for 2D is discussed in detail. By using the same procedure as in the derivation of the discretised density distribution function, we found that new lattice of four-velocity (2D) and eight-velocity (3D) models for internal energy density distribution function can be developed where the viscous and compressive heating effects are negligible. These models are validated by the numerical simulation of the porous plate 2D Couette flow problem where the analytical solution exists and the natural convection flows in a cubic cavity.