Electromagnetohydrodynamic flow and heat transfer of a non-Newtonian third grade fluid through two parallel plates of large width are studied for both heating and cooling. The plates are subjected to uniform heat fluxes. A magnetic field and an electric field are externally imposed. The effects of viscous dissipation and Joule heating are included in the analysis. The non-linear equations governing the physical situation are solved by employing the Least Square Method (LSM), a semi-analytical technique widely applied for solving nonlinearproblems. For implementing the least square method, the presence of any small parameter is not required. Non-dimensional velocity and temperature distributions are obtained and the effects of the third grade fluid parameters, Hartmann number, electric field parameter, Brinkman number on the velocity, temperature, and Nusselt number are discussed. The results imply that the Nusselt number reverses its sign when the Brinkmann number reaches a critical value. The bulk mean temperature decreases so much that the difference between the wall temperature and the bulk mean temperature becomes negative, which results in a negative Nusselt number (indicating heat transfer from the fluid). In the case of heating, the Nusselt number increases with the Hartmann number for all values of the third grade fluid parameter.