A mathematical model has been constructed for determining the effects of variable viscosity and thermal conductivity on unsteady Jeffery flow over a stretching sheet in the presence of magnetic field and heat generation. The governing partial differential equations are transformed into a set of nonlinear coupled ordinary differential equations and then solved numerically by using the Runge–Kutta–Fehlberg method with shooting technique. A critical analysis with earlier published papers is done and the results are found to be in accordance with each other. Numerical solutions are then obtained and investigated in detail for different physical parameters such as skin-friction coefficient and reduced Nusselt number as well as other parametric values such as the velocity and temperature.