This work investigates the effects of several parameters on the coefficient of performance (COP) and the specific heating power (SHP) of a coated-tube adsorber for adsorption heat pumps (AHP) suitable for water heating (space and/or domestic water heating). The COP and SHP are obtained based on physical models that have already been proven to adequately describe this type of adsorber. Several parameters are tested, namely, the regeneration, condenser and evaporator temperatures, the heat transfer fluid velocity, the tube diameter, the adsorbent coating thickness, the metal–adsorbent heat transfer coefficient, and the cycle time. Two different scenarios were tested, corresponding to distinct working conditions. The working conditions for Scenario A are suitable for pre-heating water in mild climates. Scenario B’s working conditions are based on the European standard EN16147. The maximum COP is obtained for regeneration temperatures of 75 °C and 95 °C for Scenarios A and B, respectively. The COP increases for longer cycle times (more complete adsorption and desorption processes) whilst the SHP decreases (less complete cycles by unit time). Hence, the right balance between the COP and the SHP must be found for each particular scenario to have the best whole performance of the AHP. A metal–adsorbent heat transfer coefficient lower than 200 W·m−2·K−1 leads to reduced SHP. Lower adsorbent coating thicknesses lead to higher SHP and can still provide reasonably high COP. However, low coating thicknesses would require a too-high number of tubes to achieve the desired adsorbent mass to deliver the required useful heating power, resulting in too-large systems. Due to this, the best relationship between the SHP and the size of the system must be selected for each specific application.