Horizontal wells have become quite popular for primary and enhanced oil recovery operations due to their well-documented advantages over vertical wells. Steam injection through horizontal wells has also been attempted at several places to improve heavy oil recovery. For horizontal wells undergoing steam injection, a steam chamber containing high mobility steam is established. This steam chamber, which can be of a complex shape, is surrounded by low mobility reservoir fluids. Such reservoir situations are referred to as composite reservoirs. An analytical solution for pressure transient tests for horizontal welts under composite reservoir situations with complex swept region ,shapes is not available yet. This study attempts a numerical investigation of pressure transient analysis for horizontal wells in two-region, composite reservoirs mimicking thermal recovery situations. A specialized three-dimensional, single-phase simulator was developed for this purpose. A closed, box-shaped reservoir was considered with a horizontal well. A detailed sensitivity study of transient pressure responses is presented with respect to grid size, well location in different directions, swept region shape, mobility ratio and storativity ratio. This study emphasizes the effects of the aforementioned factors on the swept volume estimation using: the pseudosteady-state method. The pseudosteady-state method is based on an analysis of a Cartesian graph of pressure response versus time. This study establishes that for horizontal wells, the swept (or inner) region volume in a two-region system can be accurately estimated by the pseudosteady-state method for large mobility and storativity contrasts between the two regions.