A study is carried out to investigate the heat transfer characteristics in peristaltic flow of Oldroyd 8-constant in a curved channel when inertial and streamline-curvature effects are negligible. The solution of resulting nonlinear governing equations is obtained using finite difference technique (FDM) combined with an iterative scheme. The impacts of physical parameters on the flow and heat transfer characteristics is investigated in detail. Particular attention is given to explain the pumping and trapping phenomena in detail. A comparative study between curved and straight channels is also made. It is found that, the rate of heat transfer increases with increasing the curvature of the channel. The current two-dimensional analysis is applicable in bio-fluid mechanics, industrial fluid mechanics, and some of the engineering fields. (C) 2015 Elsevier Ltd. All rights reserved.