Infrared thermal imaging and deep learning provide intelligent monitoring systems that detect diseases in early phases. However, deep learning models require thousands of labeled images to be effectively trained from scratch. Since such a dataset cannot be collected from a neonatal intensive care unit (NICU), deep transfer learning models and methods were used for the first time in this study to classify neonates in the NICU as healthy and unhealthy. When nine different pre-trained models (VGG16, VGG19, Xception, ResNet101, ResNet50, Inceptionv3, InceptionResNetv2, MobileNet and DenseNet201) and two different classification methods (Multilayer Perceptrons and Support Vector Machines (SVMs)) were compared, best results were obtained as 100.00% specificity, sensitivity and accuracy with VGG19, and SVMs. This study proposes highest classification performance when comparing other studies that detect health status of neonates.