Coal spontaneous combustion in underground mine goaf has a great impact on coal mining. The temperature-programmed experiment is a commonly used and effective method for studying the characteristics of coal spontaneous combustion. Aiming at the problem that the numerical simulation of coal spontaneous combustion characteristics under the condition of external air supply and temperature control in a temperature-programmed experiment is insufficient, a multi-physical field coupling numerical model of coal spontaneous combustion in the temperature-programmed experiment is established. The variation characteristics of coal temperature, oxygen, and oxidation products under external air supply and temperature control were studied. The results show that the numerical simulation results are consistent with the experimental results. With the increase in temperature, the volume fractions of oxygen and carbon dioxide decrease and increase, respectively. As the air supply volume increases, the oxygen volume fraction at the outlet increases, and the peak value of the oxygen volume fraction change rate exhibits a “hysteresis” feature, and the time corresponding to the peak value increases. Moreover, the temperature change rate increases. With the increase in the heating rate, the peak value of the oxygen volume fraction change rate increases and shows an “early appearance” characteristic, at the same time, the maximum coal temperature displays a linear increase trend.