Pipes conveying fluid is frequently applied in the oil & gas industry. Excessive flow velocity in the pipe will give rise to instability of the pipeline structure. It is highly significant to determine the critical velocity for structural stability design and safety evaluation of those pipes. In practical engineering, pipes conveying fluid is often affected by thermal load, such as heating crude oil pipeline and heating pipeline. The natural vibration frequency and critical flow velocity of pipes conveying fluid under thermal load are different from those of the ordinary flow transmission pipeline. Based on Hamilton's principle, the vibration partial differential equation of pipes conveying fluid supported at both ends under thermal load is derived. By separating variables, the equation is simplified into a univariate quartic homogeneous ordinary differential equation, the general solution is obtained according to the critical velocity conditions, and the analytical expression of critical velocity of pipes conveying fluid suitable for different boundary conditions is given. Based on numerical examples, the effects of linear thermal stress and nonlinear thermal stress on the critical velocity of pipes conveying fluid under different boundary conditions are analyzed, and compared with the results of differential quadrature calculation method to verify the accuracy of the analytical calculation method. The research demonstrated that compared with the differential quadrature method, the proposed analytical method is simpler and more accurate, and can more conveniently obtain the critical velocity of pipes conveying fluid system, which is conducive to guiding the engineering practice. Under the action of linear thermal stress and nonlinear thermal stress, the critical flow rate of the pipes conveying fluid system decreases with the increase of thermal load, and the decreasing speed is faster and faster. In the same case, the critical velocity under nonlinear thermal stress is greater than that under linear thermal stress, and the gap between them gradually increases with the increase of thermal load. Compared with the boundary conditions, it is found that the fixed boundary conditions can bear the largest thermal load. Therefore, the application of fixed boundary conditions to pipes conveying fluid system under thermal load is conducive to improve the stability of the system. The analytical method of critical velocity of pipes conveying fluid under thermal load proposed in this paper can easily and quickly obtain the accurate critical velocity in the engineering field, which provides a reference basis for the design and safety evaluation of pipes conveying fluid system under thermal load.