Oil and Gas production from HTHP reservoirs involves significant heat exchange between the wellbore fluid and its surroundings. During production, the hot fluid loses heat to the cold surroundings, continuously as it moves up the borehole. The heat transfer process impacts well-integrity and, in turn, the ability of the well to perform its required function effectively and efficiently with regard to safety and environmental factors. One often overlooked heat transfer effect is the increase in annulus pressure resulting from annular fluid thermal expansion, which can result in tubing collapse or casing burst. Damage due to high annular pressure can also dramatically affect well-integrity. During the design phase of a HPHT well, it is necessary to avoid risks and uncertainties and accurately plan the life cycle. The present work aims to investigate the nature, and predict the natural convection heat transfer coefficient in the annulus. The approach to model the natural convection heat transfer in this work is by analytical and numerical techniques. The annular space between the tubing and the casing was treated as a finite space bounded by walls and filled with fluid media (enclosures). Correlations for vertical enclosures were employed in the study. The flow field was modeled and simulated for numerical analysis, using ANSYS-FLUENT - 12 software package. Some boundary parameters have been defined by the user and fed to the software. The predicted values of Nusselt numbers from both analytical and numerical approaches were compared with those of previous experimental investigations. The results of the present work can be used for preliminary design calculations of HPHT wells to estimate rate of heat transfer from HPHT wells. This work provides a novel baseline assessment for temperature related well-integrity problems in HPHT wells. Copyright 2012, Society of Petroleum Engineers.