Thermal stress is an important factor influencing the strength of a heat exchanger tubesheet. Some studies have indicated that, even in floating-head or U-tube heat exchangers, the thermal stress at the tubesheet is significant in magnitude. For exploring the value, distribution, and the influence factors of the thermal stress at the tubesheet of these kind heat exchangers, a tubesheet and triangle arranged tubes with the tube diameter of 25 mm were numerically analyzed. Specifically, the thermal stress at the tubesheet center is concentrated and analyzed with changing different parameters of the tubesheet, such as the temperature difference between tube-side and shell-side fluids, tubesheet diameter, thickness, and the tube-hole area ratio. It is found that the thermal stress of the tubesheet of floating-head or U-tube heat exchanger was comparable in magnitude with that produced by pressures, and the distribution of the thermal stress depends on the tube-hole area and the temperature inside the tubes. The thermal stress at the center of the tubesheet surface is high when tube-hole area ratio is very low. And with increasing the tube-hole area ratio, the stress first decreases rapidly and then increases linearly. A formula was numerically fitted for calculating the thermal stress at the tubesheet surface center which may be useful for the strength design of the tubesheet of floating-head or U-tube heat exchangers when considering the thermal stress. Numerical tests show that the fitted formula can meet the accuracy requirements for engineering applications.