This paper presents a novel interferometric system for sensing the physical temperature radiated from the Earth. The proposed system consists of a Compressive Reflector Antenna (CRA) using a Y-shaped receiving array. The Compressive Reflector Antenna creates a spatial codification in the far-field of the antenna; or, by using the reciprocity theorem, it creates spatial codes in the focal plane array region when it is operating in reception mode. The sensing matrix of the system is generated by using a high frequency method based on Physical Optics, and its inversion is performed using Compressive Sensing techniques. Numerical results demonstrate the effectiveness of the proposed system for reconstructing a typical map of the physical temperature of the Earth. The proposed CRA provides similar imaging performance as that of a current state of the art system GeoSTAR; however, the former only needs one half of the horns used by the latter.