The effect of wall slip on the laminar heat transfer to power-law fluids in pipes with constant wall temperature and constant wall heat flux is investigated for the case of a short axial distance. The transformed temperature is expanded in a Leveque series in terms of the powers of s(-1/2), where s is the Laplace transformation variable with respect to the axial distance. For a constant wall temperature, the zero-order solution is the Leveque solution, whereas, for a constant wall heat flux, the first-order solution is the Leveque solution. Numerical solutions are obtained to show the convergence as well as the effect of wall slip on the Nusselt number vs the Graetz number. A significant increase in the Nusselt number is shown with an increase in the wall slip velocity. The effect of the Brinkman number is less important for high Graetz numbers.