When the high-temperature superconducting (HTS) REBCO (rare-earth barium copper oxide) coil is applied in a power system, a large amount of heat may be generated due to the short-circuiting of the system, resulting in the thermal instability of the coil. Moreover, under complex working conditions, the oscillating external magnetic field will further aggravate the coil quench. In this paper, the electromagnetic–thermal coupling model is used to analyze the loss, current distribution and temperature distribution of the REBCO coil under short-circuit fault conditions and oscillating external magnetic fields. In order to get closer to the actual situation, the modeling of the superconducting tape adopts the real tape structure, and the resistivity of the superconductor is described by the modified E-J relationship. Four cases are considered for the oscillating external magnetic field, i.e., sine, triangle, sawtooth and square cases. This model has certain significance as a reference for understanding the thermal stability of coils in extreme cases.