Themo-mechanical analysis was carried out using the finite element method for the steel shell of a cupolafurnace. When the outer surface of the shell was cooled with water to within the temperature range of 35?80°C during operation of the cupola, the inner surface of the shell was expected to exhibit a temperature of 65?248 °C based on heat transfer analysis. The shell was also expected to have an equivalent stress range of100?280 MPa in the outer surface over the temperature range examined. Upon cooling the shell to obtain anouter surface temperature <80 °C, the maximum equivalent stress of the shell did not exceed the yieldstrength. Although the temperature of the outer surface varied between 35 and 80 °C periodically due to thecooling control problem, the fatigue stress at the outer surface of the shell was calculated to be within thefatigue strength. During a non-operational period to examine the system between furnace operations, thethermal stress presented in the shell was sufficiently low to reach the desired yield strength and fatigue limit.