This paper presents a numerical performance analysis of a cylindrical heat pipe with tapered wick geometry. A 2-D numerical model is developed in COMSOL Multiphysics software and solved at steady state in order to examine the impact of wick shape on heat pipe thermal performance. The influence on crucial variables, such as axial distribution of pressure, velocity, and wall temperature, are investigated. Numerical results indicate an increase in effective thermal conductivity by approximately 62% for a tapered wick design as compared to a flat wick heat pipe, for a heat transfer rate of 455 W. This increase, however, is associated with a rise in liquid pressure drop. A novel non-dimensional parameter is proposed to predict and quantify the relationship between absolute evaporator temperature drop and liquid pressure loss. This term is coined as Temperature Pressure Index (TPI). The maximum TPI is found to be 1.81, suggesting that the decrease in evaporator temperature is more significant than an increase in liquid pressure drop.