Monitoring temperature changes of infants in the neonatal intensive care unit is very important. Especially for premature and very low birthweight infants, determining temperature changes in their skin immediately is extremely significant for follow-up processes. The development of medical infrared thermal imaging technologies provides accurate and contact-free measurement of body temperature. This method is used to detect thermal radiation emitted from the body to obtain skin temperature distributions. The purpose of this study is to develop an analysis system based on infrared thermal imaging to classify neonates who are healthy and suffering from heart disease using their skin temperature distribution. In this study, 258 infrared thermograms obtained applying data augmentation on 43 infrared thermograms captured from the Neonatal Intensive Care Unit were used. The following operations were performed: firstly, images were segmented to eliminate unnecessary details on the thermogram. Secondly, the features of the image were extracted applying Discrete Wavelet Transform (DWT), Ridgelet Transform (RT), Curvelet Transform (CuT), and Contourlet Transform (CoT) which are multiresolution analysis methods. Finally, these features are classified as healthy and unhealthy using classification methods such as Artificial Neural Network (ANN), Support Vector Machine (SVM) and Random Forest (RF). The best results were obtained with SVM as 96.12% of an accuracy, 94.05% of a sensitivity and 98.28% of a specificity.