In this study, the effects of temperature dependent viscosity and viscous dissipation on fluid flow over a moving flat isothermal plate have been investigated. A steady two dimensional laminar boundary layer flow of incompressible, Newtonian fluid past a flat plate with uniform surface velocity and temperature has been considered. The partial differential equations governing the flow have been transformed into non- dimensional form and solved using finite difference numerical method implemented in Java programing language. The numerical results obtained are presented graphically and discussed. It has been observed that increasing variable viscosity parameter increases velocity whereas it decreases fluid temperature. Increasing velocity ratio has been noted to increase fluid velocity but decreases fluid temperature. The effect of increasing viscous dissipation parameter (Eckert number) is observed to increase fluid temperature.