This paper presents a homogenized electrothermal model for high-temperature superconductor (HTS) stacks made of multiple REBCO tapes, which reduces the computational complexity of their thermal analysis. An average heat capacity and an orthotropic heat conductivity are derived for the equivalent thermal properties of the HTS coil. The proposed homogenization method is verified to produce the same results as the full model with an error below 5% for a range of scenarios, including transport losses, magnetization losses, AC frequencies from 50 to 300 Hz and a temperature range from 25 to 80 K. This new model allows for the use of a significantly coarser mesh, which reduces the computation time by an order of magnitude compared to the full model.