The transient Hartmann flow of an electrically conducting viscous incompressible non-Newtonian power-law fluid between two parallel horizontal non-conducting porous plates is studied with heat transfer, without neglecting the Hall effect. A sudden uniform and constant pressure gradient, an external uniform magnetic field that is perpendicular to the plates, and uniform suction and injection through the surface of the plates are applied. The two plates are kept at different but constant temperatures, while the Joule and viscous dissipations are taken into consideration. Numerical solutions for the governing nonlinear momentum and energy equations are obtained using finite difference approximations. The effect of the Hall term, the parameter describing the non-Newtonian behavior, and the velocity of suction and injection on both the velocity and temperature distributions as well as the dissipation terms are examined.