We present a method based on deep learning for detecting and localizing abnormal/extreme events in sea surface temperature (SST) of the Red Sea images using training samples of normal events only. The method operates in two stages; the first one involves features extraction from each patch of the SST input image using the first two convolutional layers extracted from a pretrained convolutional neural network. In the second stage, two methods are used for training the model from the normal training data. The first method uses one-class support vector machine (1-SVM) classifier that allows a fast and robust abnormal detection in the presence of outliers in the training dataset. In the second method, a Gaussian model is defined on the Mahalanobis distances between all normal training data. Experimental tests are conducted on satellite-derived SST data of the Red Sea spanning for a period of 31 years (1985-2015). Our results suggest that the Gaussian model of Mahalanobis distances outperformed 1-SVM by providing better performance in terms of sensitivity and specificity.