Natural convection in enclosed cavities is a classical benchmark for validating buoyancy-driven flow solvers and studying thermally induced instabilities. The MIT 2001 stretched cavity benchmark, solved in a 2D domain, demonstrates a transition from steady flow to a time-periodic regime with temperature oscillations near the cavity corner at elevated Rayleigh numbers, highlighting the sensitivity of thermal boundary layers to buoyancy-driven instabilities. In this work, the benchmark is extended to a commercial low-density polyethylene (LDPE) melt, representing a high-Prandtl-Number high-viscosity polymer relevant to industrial processing. To capture the viscoelastic behavior of LDPE, two constitutive models are employed: Phan-Thien–Tanner (PTT) and Giesekus. Two-dimensional CFD simulations are performed with the Boussinesq approximation for buoyancy, exploring the influence of fluid viscoelasticity on flow structure, heat transfer, and the onset of unsteady behavior. Results indicate that viscoelasticity and extremely high Prandtl number suppress or delay the corner temperature oscillations observed in low-Prandtl-number fluids such as air. Differences between the PTT and Giesekus models are observed in flow patterns, thermal boundary layer thickness, and Nusselt number distributions, demonstrating that the choice of constitutive model significantly affects predictions of heat transfer and flow instabilities. Conduction-dominated regimes prevail across most parameter ranges, emphasizing the limitations of classical air-based benchmarks when applied to high-viscosity polymer melts. This study provides new insight into the interplay between viscoelasticity, high Prandtl number, and natural convection in 2D high-aspect-ratio cavities, with relevance for the thermal design of polymer processing equipment, curing chambers, and other industrial systems. It also informs CFD validation strategies for high-viscosity, viscoelastic fluids.