Superconducting coils play a critical role in a superconducting-based nuclear fusion device. As the temperature of superconducting magnets increases with a change in current, it is important to predict their temperature to prevent excessive temperature rise of coils and operate them efficiently. We present multi-scale recurrent transformer system, a deep learning model for forecasting the temperature of superconducting coils. Our system recurrently predicts future temperature data of the superconducting coil using the previous data obtained from a multi-scale Korea Superconducting Tokamak Advanced Research poloidal field coil dataset and latent data calculated from previous time step. We apply a multi-scale temperature downsampling approach in our model to effectively learn both the details and the overall structure of the temperature data. We demonstrate the effectiveness of our model through experiments and comparisons with existing models.