A heliogyro is a rotating solar sail with the reflecting surface divided into a number of long and slender blades, which are stiffened by a spin-induced centrifugal force. Each blade can rotate around its own longitudinal axis so as to change the pitch angle and allow the thrust vector to be effectively controlled. The aim of this paper is to analyze the optimal heliocentric transfers of a Sun-facing heliogyro, that is, a heliogyro whose fundamental plane is always perpendicular to the Sun-spacecraft line. A simplified analytical model of the thrust and torque vectors provided by a Sun-facing heliogyro is illustrated, using the characteristic acceleration as a performance parameter. The proposed thrust vector model is then exploited to calculate the minimum flight times in a set of two-dimensional heliocentric transfers. Using an indirect method and a semi-analytical approach for trajectory optimization, some exemplary cases are discussed, such as circle-to-circle Earth-Mars and Earth-Venus transfers or a simplified mission to the asteroid 25143 Itokawa.