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• Heat transfer enhancement in tubes with a porous medium through pulsatile flow. • Coupled heat transfer and viscoelastic flow in a porous medium is addressed. • Pulsating flow driven by steady and periodic pressure gradients is considered. • Viscoelasticity and porous resistance jointly modify shear stress distribution. The present work investigates the influence of a viscoelastic fluid on heat transfer within a tube filled with an isotropic porous medium. For this study, the Darcy–Brinkman equation and the local thermal equilibrium are assumed to describe the viscoelastic fluid flow through the porous medium. The fluid obeys the linear Maxwell model, and its motion is produced by the superposition of a pulsatile pressure gradient. The governing equations are nondimensionalized, resulting in the emergence of the Darcy, Deborah, and angular Reynolds numbers, parameters which dominate the physics of the problem. The set of governing equations is solved analytically, while the resulting integral expressions for the Nusselt number are evaluated numerically. Unlike previous analyses, this study directly addresses the coupled interaction between heat transport and the combined influence of viscoelasticity and porous resistance. The shear stress distribution and Nusselt number are examined under the influence of porous medium and viscoelastic effects on the heat transfer. It is observed that low Darcy numbers pronounce distortions in the velocity field, which modify the mass flow rate and convective heat transfer. Due to the unsteady fluctuations of the velocity, the shear stress is distributed harmonically throughout the domain. These findings are relevant to thermal management and energy systems, particularly solar heat exchangers, providing parametric insight for engineering processes that use time-dependent pressure gradients to improve thermal performance.