Boundary layer formation over a moving or stationary surface has a wide range of applications in aerodynamics, heat transfer enhancement, and prediction of drag or resistance on a surface. Furthermore, viscosity changes with deformation cannot be ignored in almost all industrially vital fluids. Present work describes boundary layer development around a cylinder stretching axially in a shear-thinning fluid obeying Carreau model. Accompanying heat transfer problem is analyzed in the existence of frictional heating and Joule heating terms in the thermal energy equation. Previous studies concerning Carreau fluid flow driven by a stretching cylinder are discussed with a view to point out some errors concerning mathematical modeling. For computational results, a widely employed MATLAB package bvp4c is utilized, which is based on a collocation scheme. New numerical results of the resulting six parameter problem are worked out, which are utilized to assess the contribution of surface curvature on the flow fields in the presence of a shear-thinning effect. The results show that the fluid velocity is considerably enhanced for larger values of flow index behavior . In the presence of a magnetic field, momentum diffusion is significantly reduced while temperature profile is expanded.