The paper presents a numerical scheme for the open-loop optimal control of the thermoelastic deformation of space structures. The space structure response and the control loads are assumed to be periodic in time, with a given period. The numerical methodology is based on a finite element-harmonic balance procedure which is tailored with an adequate optimization scheme. Various cost functionals are considered, which involve the elastic deformation of the structure and include penalties on the control magnitudes. The performance of the thermoelastic and control schemes are demonstrated via numerical examples.