It is a crucial problem how to heat oil and save running costs for crude oil transport. This paper strictly formulates a steady-state heated oil pipeline operation problem as an explicit mixed integer nonlinear program, including consideration of two different kinds of pumps and a general hydraulic friction formulation. Different from research utilizing meta-heuristic type methods, this work presents a specifically designed branch-and-bound method called HOPBB which obtains the global optimum of the model. To achieve this, nonconvex and convex continuous relaxations of the model are proposed, which are proven to be equivalent under some suitable conditions. Meanwhile, we provide a preprocessing procedure to guarantee these conditions and introduce an outer approximation method with the warm start strategy to make the algorithm more efficient. The case study on the operation of the Q-T pipeline in China shows that our algorithm achieves a better scheme and can save 6.83% running cost compared with the practical scheme. Discussion on the effect of increasing transport temperature further gives an improvement direction which may save over 8% total operation cost. Comparisons with several commercial and open source MINLP solvers illustrate the superiority of the efficiency of the proposed HOPBB method.