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Parametric excited vibration of pipes under thermal loading may occur because the fluid is often transported heatedly.Although the stability and local bifurcation induced by the pulsating fluid velocities have attracted much research interests, the effects of thermal loading, in conjunction with the pulsating fluid dynamics, on the pipe stability and local bifurcations have rarely been studied.In this paper, the stability and the local bifurcations of the lateral parametric resonance of the pipe induced by the pulsating fluid velocity and the thermal loading are studied.A mathematical model for a simply supported pipe is developed according to the Hamilton principle.Two partial different equations describing the lateral and longitudinal vibration are obtained.The Galerkin method is applied to deduce the partial differential equations to the ordinary differential equations.The method of multiple scales and the singularity theory are utilized to analyze the stability and the bifurcation of the trivial and non-trial solutions.The transition sets and the bifurcation diagrams are obtained both in the unfolding parameter space and the physical parameter space, which can reveal the relationship between the thermal field parameter and the dynamic behaviors of the pipe.The frequency response and the relationship between the critical thermal rate and the pulsating fluid velocity are obtained.The numerical results demonstrate the accuracy of the single-mode expansion of the solution and the stability and the local bifurcation analyses.The presented work can provide valuable information for the design of the pipeline and the controllers to prevent its structural instability.