The utilization of coal resources has been improved by using the method of narrow coal pillar mining, but this leads to a stress concentration in the coal pillars, which causes differences in the oxidation of coal pillars. To study the effect of stress on the oxidation and spontaneous combustion of coal samples, programmed heating-gas chromatography coupling experiments were carried out on coal samples under different stresses, analyzing the effect rule of stress on the gas derivatives of coal samples in the process of heating and oxidation. Furthermore, the mechanism of stress influence on thermal effect parameters is explored on the basis of that analysis. The results show that the rate of oxygen consumption, CO, CO2 concentration and heat release intensity of coal samples show a changing trend, initially increasing and then decreasing with increasing stress, and these values within coal are at the maximum when the stress is 9 MPa; and with increasing stress, the activation energy shows a “V” type change and reaches the minimum of 26.89 kJ/mol at 6 MPa, which indicates that low stress promotes coal spontaneous combustion (CSC), while high stress inhibits CSC. The thermal conduction coefficient of coal samples shows a negative correlation with temperature at the low-temperature stage, while the thermal conductivity of coal samples shows a positive correlation with temperature at the high-temperature stage, and the thermal conduction coefficient of coal samples reaches a minimum at temperatures of 70 °C and 0 MPa of stress. The porosity within coal decreases, and the thermal conductivity coefficient within coal increases with increasing stress because the increase in stress makes the macromolecules within coal disassemble into small molecules, the structure becomes more compact, and the thermal conductivity increases. The study provides an important theoretical basis for better understanding the effect mechanism of stress on CSC.