In this paper, a rigorous multi-dimensional analysis is conducted upon a triple absorption heat transformer (TAHT) using the working fluids water and lithium bromide (LiBr). A full factorial design is created which determines the most influential factors affecting the system's coefficient of performance (COP), exergetic coefficient of performance (ECOP), flow ratio (FR) and total exergy destruction (E-D). The aim is to draw general conclusions which may be adopted into any such TAHT cycle and not simply be specific to any one scenario. Accordingly the paper analyses the position of each variable across its thermodynamically available range instead of the traditional selection of arbitrary temperatures. It is found that in general the condensation temperature and the pinch heat transfer gradient selected have the greatest effect, and that these should be minimised in all situations. There exist points of optimum for the temperatures of the two absorber-evaporators within the cycle, however the evaporation temperature has conflicting effects for different dependent variables, and must therefore be selected based on an economic analysis. The results of this study also show that the generator is the source of the largest exergy destruction in the cycle, followed by the two absorber-evaporators. (C) 2013 Elsevier Ltd. All rights reserved.