The laminar boundary layer flow and heat transfer for multiphysical transport of an optically dense Casson non-Newtonian fluid along an isothermal horizontal circular cylinder embedded in a variable-porosity medium in the presence of thermal and hydrodynamic slip conditions is analyzed. Non-Darcy effects are simulated via a second-order Forchheimer drag force term in the momentum boundary layer equation. The cylinder surface is maintained at a constant temperature. The boundary layer conservation equations, which are parabolic in nature, are normalized into nonsimilar form and then solved computationally with an efficient, implicit, stable Keller-box finite-difference scheme. Increasing velocity slip consistently enhances temperatures and reduces velocity throughout the boundary layer regime. An increase in thermal slip parameter strongly decelerates the flow and also reduces temperatures in the boundary layer regime. Increasing porosity is found to elevate velocities, that is, accelerate the flow, but decrease temperatures, that is, cool the boundary layer regime. Thermal radiation parameter (inversely proportional to radiative flux contribution) is seen to reduce both velocity and temperature in the boundary layer. Local Nusselt number is also found to be enhanced with increasing radiation parameter. Temperatures are, however, very slightly decreased with increasing values of Casson non-Newtonian parameter. The study is relevant to processing of plastics in industry. © 2016 by Begell House, Inc.