Peristaltic pumping of non -Newtonian fluid generally arises in physiological and engineering applications. The study of the peristaltic transport has become quite interested to several scientists because of its various applications in science and engineering. The objective of the present study is to discuss the peristaltic transport of a Jeffrey fluid with temperature - dependent viscosity in an endoscope (modelled as cylindrical annulus) with partial slip. The effect of variable viscosity in a Jeffrey fluid flow associated with partial slip was not considered till to date. We considered the Vogel's viscosity model. The expressions for temperature, velocity and stream function was obtained by using regular perturbation method in terms of small viscosity parameter. We investigated that the pressure rise decreases with increasing Jeffrey parameter. Graphical effects are presented understand the physical characteristics of different parameters. © 2020 Author(s).