This study numerically investigates the temperature distribution in a conduction-cooled ReBCO magnet during ramping operation. Firstly, the analyzed magnet is electromagnetically designed to generate a central magnetic field of 4 T at the ramp rate of 0.2 T/s. The two-dimensional thermal network model is developed in this paper to solve the transient heat diffusion equation within the winding pack of the magnet, considering thermal contact conductance. The thermal design show that, despite a sufficient current margin provided at the electromagnetic design stage, the localized temperature rise induced by the hysteresis loss degrades the critical current, making the magnet unstable. To address this issue, the installation of thermal drains between the winding layers is proposed, and its effectiveness is evaluated. Detailed methodology and analysis results are presented and discussed in the paper.