Until now, mesoscale oceanic eddies have been automatically detected through physical methods on satellite altimetry. Nevertheless, they often have a visible signature on Sea Surface Temperature (SST) satellite images, which have not been yet sufficiently exploited. We introduce a novel method that employs Deep Learning to detect eddy signatures on such input. We provide the first available dataset for this task, retaining SST images through altimetric-based region proposal. We train a CNN-based classifier which succeeds in accurately detecting eddy signatures in well-defined examples. Our experiments show that the difficulty of classifying a large set of automatically retained images can be tackled by training on a smaller subset of manually labeled data. The difference in performance on the two sets is explained by the noisy automatic labeling and intrinsic complexity of the SST signal. This approach can provide to oceanographers a tool for validation of altimetric eddy detection through SST.