The paper investigates thermo-fluidics and entropy generation for a couple stress Casson fluid flow in a porous medium channel composed of two parallel stretching walls. Both the walls maintained at different temperatures stretch linearly in their own planes. The flow set-up caused by the entrainment of the fluid by the stretching walls and temperature difference constitutes a sixth-order nonlinear boundary value problem after similarity transformation. Two different methods viz. Differential Transform Method and Runge–Kutta Fehlberg Method are exploited to treat the system analytically as well as numerically. The effects of pertinent parameters on coefficient of skin friction, Nusselt number, velocity, temperature and inherent thermodynamic irreversibility are shown by tables and graphs and discussed. It is found that the skin friction and Nusselt number increase substantially with increasing values of characteristic length and couple stress parameter and decrease with the increasing values of permeability and Casson parameter, respectively. The computations have been carried out on the MAPLE programming language.