This paper presents the development and application of a numerical model to predict the temperature distribution of the vertical borehole system during circulation and shut-in conditions. The presented model can simulate the transient temperature disturbances of the drilling fluids, the drill string, the casing strings, the cement behind the casing, and also the surrounding rock formation. The transient temperature profiles resulting from the presented model are compared with a CFD (Computational Fluid Dynamics) model using ANSYS-FLUENT. A good agreement between the results of both models is found. However, the developed model has a great advantage over the CFD model in terms of computation time and power. In addition, a comparison with field results showed a good agreement between the simulated temperature and the experimental data using the presented model. Moreover, a sensitivity analysis on the influence of the size and length of the bottom hole assembly (BHA) on the temperature of the borehole is performed. The analysis is performed for both static and dynamic conditions. The results showed a significant influence of the BHA size on the static and dynamic bottom hole temperature. However, the length of the BHA only affects the dynamic bottom hole temperature.