An analysis is carried out to determine the distribution of surface temperature along a flat plate experiencing simultaneous convective heat transfer, radiative exchange with the environment, aerodynamic heating, and internal heat sources or sinks. Both laminar and turbulent boundary layer flows are considered. Numerical results are presented for a wide range of the governing parameters; these are compared with simplified solutions based on local application of heat-transfer coefficients for uniform wall temperature and for uniform heat flux. The problem is treated within the framework of the thermal boundary layer with prescribed heat flux. The initial part of the paper is devoted to establishing certain general results for such boundary layers. Exact solutions are obtained for power-law and series heat flux distributions. An approximate solution for arbitrarily varying surface heat flux is derived by superposing step-function solutions furnished by the integral energy equation.