The work presents measurements of the length stability of Zerodur glass ceramic with temperature change. Measurement of this thermal characteristic is necessary for determination of the optimal temperature at which the Zerodur glass ceramic has a coefficient of thermal expansion close to zero. The principle of the measurement is to monitor the length changes using an optical resonator with a cavity mirror spacer made from the Zerodur material to be studied. The resonator is placed inside a vacuum chamber with a temperature control. A tunable laser diode is locked to a certain optical mode of the resonator to monitor the optical frequency of this mode. A beat-note signal from optical mixing between the laser and a stabilized femtosecond frequency comb is detected and processed. The temperature dependence of the glass ceramics was determined and analyzed. The resolution of the length measurement of the experimental set-up is on the order of 0.1 nm.