The aim of this paper is to study an optimal control problem for a parabolic solar collector. We consider a bilinear distributed model, where the control models the velocity of the heat-transfer fluid. We prove the existence of an optimal control, and we derive a necessary optimality condition. Then we give an algorithm for the computation of the optimal control. The obtained results are illustrated by simulations of the collector model, using data of Ain Beni Mathar solar plant in Morocco.