Perturbation methods are used to study steady, fully developed flow of Oldroyd-B fluids through a curved pipe of circular cross-section. A perturbation solution up to secondary order is obtained for a small value of curvature ratio. The range of validity of the perturbation method are discussed and chosen carefully. Variations of temperature distribution with Re and We are discussed in detail in order to investigate the combined effects of the two parameters on temperature distribution. Present studies also show the variations of the heat transfer rate with Re and We. This study explores many new characteristics of convective heat transfer of a kind of viscoelastic fluid through curved pipes. (C) 2007 Elsevier Ltd. All rights reserved.