A solar sail is a lovely way to conduct near-solar research, where its effectiveness is particularly high. The paper aims to study the possibility of controlling the sail temperature by deflecting its surface from the radiation flux. We consider the non-planar motion of a spacecraft with an imperfect solar sail, subject to the disturbances in the nearest Sun vicinity: the relativistic effects, the deviation of the form of the electromagnetic field of solar radiation from the point-source electromagnetic field, and changes in the optical characteristics of the sail material due to changes in temperature and surface degradation.