High-temperature superconductors such as REBa2Cu3O7-x (REBCO, RE = rare earth) can generate strong magnetic fields that are promising for applications in particle accelerators and compact fusion reactors. Traditionally, voltage taps are installed in superconducting magnets to measure the voltage signals due to resistive transitions. The voltage-tap-based diagnostics is important for the development of magnet technology as it can help pinpoint the locations in the magnet windings that limit the magnet performance. The architecture of the multi-tape REBCO cable such as CORC wires, however, makes it difficult to apply the voltage-tap-based diagnostics to identify the locations of resistive transitions. Distributed fiber optic sensing (DFOS) has the potential to address this issue. In this paper, we report the measurements of thermal strain along a CORC wire based on optical frequency domain reflectometry with a maximum spatial resolution of 0.65 mm and a temporal resolution of 10 Hz. The optical fiber is co-wound with the CORC wire that is epoxy impregnated. During the test, current was increased until a resistive transition occurred in the conductor. The spectrum shift of the reflected light along the fiber was recorded. The results suggested that with proper thermal isolation from the cryogen, DFOS can be used to identify the locations of resistive transitions in CORC wires and magnets. The results will allow a better understanding of the causes of resistive transitions in REBCO conductors and magnets, which will help improve the REBCO magnet technology.