The GMT-Consortium Large Earth Finder (G-CLEF) will be part of the first generation instrumentation suite for the Giant Magellan Telescope (GMT). G-CLEF will be a general purpose optical passband echelle spectrograph with a precision radial velocity (PRV) capability of 10 cm/sec, a requirement necessary for the detection of Earth analogues. The instrument will be particularly sensitive to thermal effects and the necessary stability cannot be achieved through the use of low CTE materials alone. It is the combination of low CTE materials and exquisite thermal control which will enable the instrument to achieve its precision requirements. G-CLEF will complete its Critical Design phase in mid-2018. In this paper, we discuss the precision thermal control systems which enable milli-Kelvin-level stability of the spectrograph and its red and blue focal planes. The measurement electronics and thermal control strategies used in the spectrograph are described. Of particular importance is the development of a continuous LN2 flow cryo-cooler system used to maintain the focal planes at stable cryogenic operational temperatures. This system has been validated with a prototyping effort completed during the instrument’s design phase. We also review G-CLEF’s insulated enclosure which simultaneously maintains the spectrograph a stable temperature and limits the maximum thermal leakage into the telescope dome. This work has been supported by the GMTO Corporation, a non-profit organization operated on behalf of an international consortium of universities and institutions: Arizona State University, Astronomy Australia Ltd, the Australian National University, the Carnegie Institution for Science, Harvard University, the Korea Astronomy and Space Science Institute, the São Paulo Research Foundation, the Smithsonian Institution, the University of Texas at Austin, Texas AM University, the University of Arizona, and the University of Chicago.