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In this article, the boundary layer analysis which can be used to educate engineers and scientists on the flow of some fluids (i.e. glossy paints) in the industry is presented. The influence of melting heat transfer at the wall and thermal stratification at the freestream on Upper Convected Maxwell (UCM) fluid flow with heat transfer is considered. In order to accurately achieve the objective of this study, classical boundary condition of temperature is investigated and modified. The corresponding influences of thermal radiation and internal heat source across the horizontal space on viscosity and thermal conductivity of UCM are properly considered. The dynamic viscosity and thermal conductivity of UCM are temperature dependent. Classical temperature dependent viscosity and thermal conductivity models were modified to suit the case of both melting heat transfer and thermal stratification. The governing nonlinear partial differential equations describing the problem are reduced to a system of nonlinear ordinary differential equations using similarity transformations and solved numerically using the Runge-Kutta method along with shooting technique. The transverse velocity, longitudinal velocity and temperature of UCM are increasing functions of temperature dependent viscous and thermal conductivity parameters. This could increase the efficiency of some fluids flow in the industry. Effects of selected emerging parameters on the velocity and temperature fields are plotted and discussed.