The fast and accurate evaluation of the degree of thermal damage still remains a key factor in the decision-making process but the accuracy of diagnosis is limited by the subjectivity of the clinical knowledge. The current study is aimed at the examination of the deep learning approach towards the automated classification of the skin burns into three degrees using CNNs and transfer learning approaches. A carefully curated dataset of 1,221 burn images was prepared using resizing, normalization, and data augmentation. Additionally, the class weighting approach was used in order to overcome the problems associated with the skewness of the data. The comparison of four different architectures was conducted including CNN, MobileNetV2, EfficientNetB0, and ResNet50 using ImageNet pre-trained weights. Experimental results indicate that ResNet50, tuned using the two-stage training approach, performed best, with test accuracy of 81.81%, precision 0.92, recall 0.90, and F1 score 0.91. The custom CNN model was unable to exhibit stochastic convergence, achieving baseline accuracy of 42.57%, whereas MobileNetV2 and EfficientNetB0 delivered moderate results with 50.89% and 61.65%, respectively. Confusion matrix analysis reveals that the residual learning structure generalized well in all levels of severity, including the important minority class of third-degree burns. The results indicate the dominance of deep residual networks in classifying medical images with insufficient data. The results suggest the use of transfer learning in burn assessment support systems.