The temperature evolution of GdFeCo electrons following optical heating plays a key role in all optical switching of GdFeCo and is primarily governed by the strength of coupling between electrons and phonons. Typically, the strength of electron-phonon coupling in a metal is deduced by monitoring changes in reflectance following optical heating and then analyzing the transient reflectance with a simple two-temperature thermal model. In a magnetic metal, the change in reflectance cannot be assumed to depend only the electron and phonon temperatures because a metals reflectance also depends on the magnetization. To deduce the electron-phonon coupling constant in GdFeCo, we analyze thermal transport in Au and GdFeCo bilayers following optical heating of the GdFeCo electrons. We use the reflectance of the Au layer to monitor the temperature evolution of the Au phonons. By interpreting the response of the bilayer to heating with a thermal model, we determine the electron-phonon coupling constant in GdFeCo to be 6 x 10^17 W/(m^3-K) corresponding to an electron-phonon relaxation time in GdFeCo of ~150 fs.