Temperature gradient focusing (TGF) is a recently developed technique for spatially focusing and separating ionic analytes in microchannels. The temperature gradient required for TGF can be generated either by an imposed temperature gradient or by joule heating resulting from an applied electric field that also drives the flow. In this study, a comprehensive numerical model describing the joule heating induced temperature development and TGF is developed. The model consists of a set of governing equations including the Poisson-Boltzmann equation, the Laplace equation, the Navier-Stokes equations, the energy equations and the mass transport equation. As the thermophysical and electrical properties including the liquid dielectric constant, viscosity, and electric conductivity are temperature-dependent, these governing equations are coupled, and therefore the coupled governing equations are solved numerically by using a CFD-based numerical method. The numerical simulations agree well with the experimental results, suggesting the valid mathematical model presented in this study.