Abstract: During the period of shutdown of a heated crude oil pipeline, the temperature drop of oil will make its viscosity rise and even results in the frozen pipeline. That will cause difficulty for restart of pipeline. The accurate temperature computation and solidifying simulation of oil in pipeline are therefore essential both for estimating maximum allowable solidifying time of shutdown and making restarting strategy of pipeline. In the light of the interaction of oil, pipeline and ambient media and their unstable heat transmission, a mathematical model for thermal calculation considering temperature dependent relative physical properties and phase change of oil is set up. By conformal transformation and cassette integration, this model can be used to do a series of numerical calculations, analyze the cooling and solidifying law of the oil upon shutdown. As examples, the oil temperature change and solidifying process have been calculated by using this method, and satisfactory results have been obtained. Comparing this method with the others introduced in the reference and the measured results indicates that the model and algorithm derived here are more reliable.