Optimal control of viscoelastic fluid flow in a 4 to 1 contracting channel is investigated. The control mechanism is based on heating or cooling the fluid along a portion of the boundary of the flow domain. In order to perform the control, a nonisothermal model for viscoelastic fluids is used consisting of the PTT model with relaxation time and elastic viscosity depending on temperature (following an exponential dependency, the WLF model). Moreover, the momentum, mass and constitutive equations are coupled with the heat equation forming the so-called primal system. The goal of the control is to find an optimal temperature on the boundary of the domain such that the large recirculation zones at the corners of the contracting channel are reduced and the fluid behaves like a viscous one. Two different cost functionals are used to reach this goal: one of tracking type, the other penalizing negative contributions of the velocity component in direction of the span of the channel. The minimization of these cost functionals is achieved with a gradient algorithm. An optimality system, derived by the use of the Lagrange multipliers, allows us to deduce this optimal control. The primal and dual systems are solved using the same numerical method: a finite differences discretization on staggered grids, a decoupling approach and the Gauss-Seidel solver with a multigrid algorithm. Numerical simulations are performed with a Weissenberg number equal to 10. We succeed in reducing the recirculation zone by applying the correct boundary temperature. (C) 2000 Elsevier Science B.V. All rights reserved.