The precise machine components' deformation is resolved and compensated by thermal expansion, but because of its coefficient's accuracy and the compensated results have a few errors. By using the available precision measuring system composed of mechanical,electrical and optical installation, which can control temperature and measure main geometrical parameters. We study the thermal expansion behavior of the ball square axis under the common range of temperature : 5-45℃ and find that thermal deformation coefficient of ball shape has no connection with the fringe conditions. So a new definition-thermal deformation coefficient, which will take the place of the thermal expansion coef ficient,has been proved to be more rational and accurate.