Reynolds equation is the pre-dominantly used PDE for modelling the fluid flow or more accurately the fluid pressure in an elastohydrodynamic lubrication (EHL) contact. The equation is derived by combining the two conservation equations of momentum and continuity into a single equation for the fluid pressure. The numerical approach for theoretical investigations performed on EHL contacts in this work is somewhat different. The modelling of the fluid flow is based on a computational fluid dynamic (CFD) technique. The fluid flow is simulated by aid of the equations of momentum and continuity in a more complete form and when the thermodynamics is incorporated, the equation of energy. The aim of the investigation was to examine whether the CFD technique could be used to handle thermal transient rough EHL line contacts. It is shown that commercial CFD software can be modified to meet such requirements. The influence of thermal effects on the flow under sliding motion was investigated. The non-Newtonian model used in this work is the Ree-Eyring model. It is shown that the choice of the Eyring stress in the model influences flow in the contacts. If the thermal properties of the surrounding solids differ, it has been shown experimentally and theoretically that a dimple or increased central film thickness may appear in the EHL contacts. This work shows that the governing mechanisms that result in the dimple are also present in thermal transient rough EHL line contacts.