Heat transfer analysis coupled with peristaltic transport is important in many real-world application areas varying from microchannels to spacecrafts. Power production, chemical, and food industries, electronics, and environmental engineering are some examples of applications. In thermal devices, the overall performance of a heat exchanger depends on heat exchanger efficiency and entropy generation. The main purpose of this paper is to study a mathematical model coupling the peristaltic pumping with the heat transfer phenomenon for an incompressible Newtonian fluid in an elliptical tube. The Navier-Stokes and energy equations have been analytically solved for long wavelength, small Reynolds, and small Peclet numbers approximations. Exact expressions of velocity profile and temperature distribution have been found in the wave frame analysis. The impacts of pertinent parameters on the physical quantities of the problem have been analyzed with the help of graphs. We concluded that the geometrical parameters (occlusion, aspect ratio) enhance the pressure rise and the mechanical efficiency. It should be noted that the best way for minimizing entropy generation is decreasing occlusion, aspect ratio, flow rate, or Brinkman number.