Analysis based on first and second law of thermodynamics together with direct and artificial neural networks inverse (ANNi) have been used to develop a methodology to decrease the total irreversibility of an experimental single-stage heat transformer. With the proposed methodology it is possible to calculate the optimal input parameters that should be used in order to operate the heat transformer with the lower irreversibilities. Mathematical validation of ANNi was carried out together with the comparison between the total cycle irreversibility (I(cycle)) obtained thermodynamically and the I(cycle) determined by using the ANNi. The results showed a mean discrepancy of 0.9% of the I(cycle) values. The proposed new methodology can be very useful to control on-line the performance of a single-state heat transformer obtaining lower I(cycle) values. (C) 2010 Elsevier Ltd. All rights reserved.