The quench and recovery characteristics of two GdBCO-coated conductor racetrack coils, one wound onto a high-strength aluminum (AL 6061-T6) bobbin and the other wound onto an oxygen-free high-conductivity (OFHC) copper bobbin, were evaluated to investigate the effect of bobbin material on the thermal stability of the HTS racetrack coil. The test results show that the minimum quench energy values of the coil wound onto the OFHC copper bobbin were larger than those of the coil wound onto the AL 6061-T6 bobbin. Furthermore, in the case of the coil wound onto the OFHC copper bobbin, the voltage signals increased more slowly compared to the coil wound onto the AL bobbin, and the recovery time was much shorter after a hot spot was generated by a heater. Overall, the coil wound onto the OFHC copper bobbin exhibited better thermal stability due to its superior thermal diffusivity.