Casing design projects must ensure well integrity throughout its life, which can be as long as several decades. An important load to be considered appears as a consequence of production. During production, the annuli became heated from the transfer of bottom hole temperature up the well by the produced fluids. With heat-up, the fluids trapped in the annulus began to thermally expand. The expansion induces a volume enlargement, which is restrained by the stiffness of the well structure. This resistance to fluid free expansion keep the fluid confined and can produce a substantial pressure increase. In some cases, pressure may become so great that it can collapse casing, leading to well abandonment and large losses. This pressure increase phenomenon is well-known in the oil industry as annular pressure build-up (APB). In the present study, a monophasic state-state thermal model was developed to determine the oil temperature profile in the tubing and the temperature profile in all structures of the well. As casings are not perfectly rigid, temperature and pressure increase in the well results in annular volume change. Because the well consists of a sequence of casing strings that define the well annuli, the modeling of casing strains should be based on a systematic approach that considers the interaction among the various strings. The study compares results to those obtained with a commercial computer application, presenting good agreement. Further, a sensitivity analysis is performed to provide a better understanding of the phenomenon.