A theoretical comparison of neural network (NnM) and thermodynamic (ThM) models is carried out to estimate on-line the coefficient of performance (COP) in an absorption heat transformer integrated with a water purification process (AHT-WP). The NnM has been computed for 16 variables measured by sensors (input and output temperatures for each of the four components absorber, generator, evaporator and condenser; input pressure parameters and LiBr + H2O concentrations). The ThM estimates the COP values with average temperatures of each component of the AHT-WP. This ThM has been designed for steady-state conditions while the NnM has been developed for steady- and unsteady-state conditions. Both models can be used to calculate the COP values on-line; nevertheless, each model has its own advantages and disadvantages in the AHT-WP design and control. The waste heat simulated for the experimental water purification system is lower than I kW, while temperature and lithium bromide concentration are invariable in huge systems.