The radiative peristaltic flow of Powell–Eyring nanofluid with temperature-dependent viscosity in an asymmetric channel is considered. Mathematically, nonlinear radiation is accounted through Stefan–Boltzmann law. The governing equations with the appropriate constitutive equations for the non-Newtonian fluid are modeled in the wave frame of reference. Contrary to viscous fluid with linear radiation, these equations are highly nonlinear in nature. Semi-numerical solutions are obtained under well-established large wavelength and small Reynolds number approximations. Important features of fluid flow and heat transfer are discussed graphically for various physical parameters highlighting the influence of nonlinear radiation and variable viscosity.