Abstract: In the present study, solution methods for velocity and temperature fields of incompressible fluids are developed. The mathematical characteristic of governing flow equation used for incompressible fluids is changed from elliptic dominated to hyperbolic dominated, by applying artificial compressibility concept. Resorting to the pseudo-compressibility concept, the continuity constraint is perturbed by the time derivative of pressure. In this study, to calculate convective fluxes, Roe Riemann solver is applied to the equation and the required coefficients are derived for both velocity and temperature fields of artificial compressible flows. The discretized equation are solved by an explicit 5th order Runge-Kuta time stepping scheme which is found to be efficient in terms of convergence rate and stability. Faster convergence is achieved by applying local time stepping. The equation are discretized in finite-volume cell-centered approximation. The method is verified by solving fluid flow over circular cylinder and lid driven cavity and comparing the results with those available in literature. Finally, the convergence rate of the developed method is compared with the averaging method, in which the current method shows a noticeable reduction in iteration steps.