We present measurements of the coefficient of thermal expansion (α) of an all-sapphire, cryogenic, Fabry-Perot optical cavity between 5 K and 77 K. The cavity is to be used as a secondary optical frequency reference. Measurements were made by tracking the frequency of the cavity relative to a free-running Nd:YAG non-planar ring laser. We find that α = (1.56 ± 0.84) 10 - 1 2 T ( 3 . 0 ± 0 . 2 ) [K - 1 ].