Gas transmission pipes are required to have sufficient material toughness at their minimum working temperature, (here, called Minimum Design Metal Temperature, MDMT) to avoid brittle fracture. This paper proposes a new practical approach in predicting the MDMT for buried natural gas transmission pipes. This approach is based on a thermal-hydraulic mathematical model to simulate the conjugate heat transfer through the pipe metal, the gas flow inside the pipe, the soil medium surrounding it, and ambient. For the gas flow inside the pipe, a 1D thermal-hydraulic model was utilized to simulate the convective heat transfer, Joule-Thomson effect, and heating of the gas due to pipe wall friction. Using computational simulations in conjunction with regression analyses, a simplified analytical model was developed to predict the temperature field in the surrounding soil for the parameter ranges of interest, including time-varying ambient air temperature. This model was then incorporated as a boundary condition in the 1D thermal-hydraulic gas flow model above to reflect the thermal interaction among the ambient air temperature, soil medium, pipe metal, and the gas flow inside the pipe. Based on the results, daily average ambient temperature data results in the same soil temperature as the hourly data. The initial soil temperature distribution also affects MDMT prediction. The model has been successfully validated against numerical analysis studies in the literature. The proposed approach can replace the transient computational fluid dynamics (CFD) simulation for practical MDMT prediction in pipelines.