Wickless heat pipe heat exchangers (HPHE) consistently showed instabilities and omits many experimental tests. The performance of a heat pipe is governed by many parameters, and the effects of which may influence each other. The objective of this paper is to develop a new approach for an air–air heat pipe heat exchanger that takes into consideration the effect of heat transfer coefficients, saturation temperature, and thermal resistances inside the heat pipes as well as maximum heat transfer limit. The approach is based on analyzing inner heat pipe parameters with HPHE external working conditions. Results are also assessed for higher heat capacities ratio and found that the thermal resistances inside a heat pipe are a limiting factor, leading the HPHE system to perform poorly in particular for Cr ≤ 1. Overall heat transfer coefficients at HPHE sides as well as HPHE effectiveness as a function of Cr are assessed. Trying to follow the Chaudourne (1992, “The Heat Pipe Heat Exchangers: Design, Technology and Applications,” Design and Operation of Heat Exchangers, Springer, Berlin, Heidelberg, pp. 386–396) profile for conventional heat exchangers, HPHE effectiveness is determined and limited to 0.5 number of transferred units. The established model is verified by the existing literature and demonstrates numerical results that agree with the experimental data within a 2.86% error.