The heat transfer of orbiting scroll wrap in an air scroll compressor under steady operation is simplified as a two-dimensional heat conduction problem with periodic moving convection boundary conditions. The heat conduction equation and the equivalent initial condition are obtained in a body-fitted coordinates system constructed by the normal angle and the normal component of the scroll profile. To solve the numerical temperature model with the discrete form based on the control volume method, a new iteration method was developed. The numerical analysis cases involving two orbiting scroll wraps, thin and thick scroll wraps, show that the temperature is uniform along scroll wrap thickness, and can therefore be represented by the mid-area temperature of the scroll wrap. The temperature increases linearly with the increasing normal angle and involute angle. The temperature is almost invariable with the orbiting angle and so that can be considered to be steady in engineering practice. (C) 2013 Elsevier Ltd. All rights reserved.