The effects of viscous heating on torsional flow of viscoelastic fluids in the parallel-plate viscometer are considered. The fluid is modelled by the Oldroyd-B constitutive equation with temperature-dependent viscosities and relaxation time which obey a Nahme type law. Analytic solutions are obtained in the limit of small Nahme-Griffith number which are uniformly valid up to the fluid-air interface. If the aspect ratio, a is small then there is a thermal boundary layer of width a at the free surface. (C) 2003 Elsevier Science B.V. All rights reserved.