An analysis has been carried out to determine the momentum and heat transfer occurring in the laminar boundary layer on a continuous moving surface which has an arbitrary surface velocity and nonuniform surface temperature. Merk series types of solutions are obtained for the momentum and heat transfer for an isothermal surface. The results are expressed in terms of universal functions. For a nonisothermal surface, the procedure begins with a consideration of the solution of the energy equation for a step discontinuity in the surface temperature by the introduction of appropriate transformation variables. Equations for the temperature profile and for the local heat flux are expressed explicitly in terms of the Prandtl number and the surface velocity parameter. Numerical examples for a power law surface velocity and a linearly stretching surface velocity with nonzero slot velocity are given for the isothermal surface. The accuracy of the present solutions is also discussed.