This paper presents numerical applications of a finite-volume method to steady three-dimensional non-isothermal inertial flows in geometries related to a single-screw extruder with the purpose to provide characteristic curves related to rheological parameters, geometrical and operating conditions. We consider incompressible fluids obeying Newtonian, non-Newtonian Carreau-Yasuda equations with different shear-thinning properties. The temperature dependence is described by a Williams-Landel-Ferry (WLF) equation. For discretizing the equations and unknowns, we use a staggered grid and solve the set of governing equations by a decoupled algorithm. The numerical results are presented in different gap conditions and allow us to state the rheological parameters, the screw parameters and the rotational velocity on the flow characteristics in a screw-barrel system.