The paper presents analytical solutions for the flow and heat transfer in a steady laminar boundary flow of an electrically conducting fluid of second grade subject to a transverse uniform magnetic field past a semi-infinite stretching sheet with power-law surface temperature or power-law surface heat flux. The effects of viscous dissipation, internal heat generation or absorption, work done due to deformation and Joule heating are considered in the energy equation. The variations of surface temperature gradient for the prescribed surface temperature (PST case) and surface temperature for the prescribed surface heat flux (PHF case) with various parameters are graphed and tabulated. Asymptotic solutions of the temperature for large Prandtl number are also given for two heating conditions. The inclusion of the Joule heating has a significant influence on the thermal characteristics at the wall especially when the Eckert number, magnetic parameter as well as the Prandtl number are large. When the Eckert number is large enough, the heat may flow from the fluid region to the wall in contrast to that when Eckert number is small. A physical explanation is proposed for this phenomenon. (C) 2004 Elsevier Ltd. All rights reserved.