Viscosity is an essential parameter of fluid physical properties for assaying the heat transfer whendesigning a nanofluid system. For this purpose, this article investigates the effect of temperature dependent viscosity on the peristaltic flow of Jeffrey nanofluid in an asymmetric channel. For peristaltic literature, this model is progressed for the first time. This model of nonlinear partial differential equation is reformulated under the assumption of long wavelength and low Renolds number, and solved semi-analytically with the aid of multi-step differential transform method (Ms-DTM). Semi-analytical solutions have been evaluated for the pressure gradient as well as the distributions of velocity, temperature and nanoparticles concentration. Moreover, numerical integration is also operated to assess the expressions for pressure rise. Two cases of temperature dependent viscosity are deliberated. Case (I), all non-dimensional parameters that are functions of viscosity, have been regarded as constant within the flow. Case (II), these acknowledged parameters are then supposed to vary with temperature. We have made a detailed comparison between the two cases, and unrealistic results have been found, although case (II) accepts the experimental results. Excellent agreements are found between the semi-analytical results of the present paper and the existing published results, by taking ðb ¼ 0Þ and Da¼1. In case (II), decrement in variable viscosity parameter b cause to enlarge the temperature of fluid. As the molecules of oil, the increase in temperature acquire it more energy and make them moves more freely, which is the main idea of crude oil refinement, where crude oil is converted and refined into more desirable products such as petroleum naphtha, gasoline, kerosene and heating oil.