Numerical simulations for the non-isothermal flow of a nylon-6 fluid passing over a transverse slot with heat dissipation are considered with a differential-type non-isothermal White-Metzner model describing the non-Newtonian behavior of the melt. The results obtained in the study are computed by using the elastic-viscous split-stress finite element method incorporating the non-consistent streamline-upwind scheme. As a verification of the numerical scheme, the algorithm is first applied to compute the corresponding isothermal flow of the upper-convected Maxwell fluid, a special case of the melt, characterized by constant viscosity and relaxation time. Hole pressure was evaluated for various Deborah numbers (De), and compared with that derived from the Higashitani-Pritchard (HP) theory. The agreement between the two is found to be satisfactory for creeping flow in the De range for which the HP theory is valid. Subsequently, hole pressure and other flow characteristics were predicted. Furthermore, the effects of heat-transfer, shear-thinning, and slot geometry on hole pressure were also investigated.