Abstract <p>The investigation and comprehension of heat transport, encompassing variations in thermophysical variables such as thermodynamic and conductive temperatures, strain, displacement, and stress within biological tissues and organs, hold crucial importance in medical thermal therapeutic applications, such as the treatment by hyperthermia and thermal ablation. This study analyzes the effect of moving heat source with constant velocity on a finite-length skin tissue using the Pennes heat conduction equation within the framework of the two-temperature theory. The Modified-Green-Lindsay model, incorporating thermal relaxation and strain-temperature rate effects, is employed alongside comparisons with the Green-Lindsay and Lord-Shulman models. Constitutive relations and governing equations are formulated, with solutions obtained in the Laplace transformed domain and estimated numerically via the Honig Hirdes algorithm. The results, presented graphically, demonstrate the significant influence of the two-temperature parameter and heat source velocity on the field variables, offering valuable insights into thermoelastic behavior in medical applications.</p>