Nowadays, as a result of the globalisation of epidemics, serious progress is being made in the vaccine sector. However, the storage and distribution of these vaccines to countries is as important as their production. At the same time, more human loss is caused by cancer diseases. It is important to examine cancer cells and to store them under appropriate conditions for studies in this field. In this sense, the cooling cycle is a system that can be used to store vaccines and some types of cancer cells in suitable conditions. This work analyses numerically the energy behaviour of a storage unit designed to be used with R134a, R1234yf, R502, and R717 at low temperatures between 201K and 259K. These data were examined with the help of mathematical formulations of thermodynamics to make an exergy analysis using Engineering Equation Solver (EES) program. Additionally, these applications of energy analysis are important and necessary in terms of sustainability and climate change. For this reason, the Artificial Neural Network (ANN) model was used to forecast different types of energy efficiency problems; a method capable of identifying complex non-linear relationships between input and output data sets. This study proposes a new procedure to identify the structure and parameters of the hidden layer, which can apply the feedforward ANN model to the model and proves the potential of this type of model for thermodynamic values. We compare a model based on an artificial neural network (ANN) with a model based on the principles of thermodynamics as an audit and prediction tool to predict exergy destruction of the cooling cycle system by applying different neural network architecture types. This ANN is trained by using temperature and mass flow as inputs. The results obtained from the method are also compared to the input-output model predictions with good accuracy.