The Chao and Fagbenle’s modification of Merk series has been employed for the analysis of forced convection laminar thermal boundary layer transfer for non-isothermal surfaces. In addition to the Prandtl number (Pr) and the pressure gradient (∧), a third parameter (temperature parameter, γ ) was introduced in the analysis. Solutions of the resulting universal functions for the thermal boundary layer have been obtained for Pr of 0.70, 1.0 and 10.0 and for a range of ∧ . The results obtained for the similarity equations agreed with published results within very close limits for all the ∧’s investigated.