Temperature is an essential oceanographic variable (EOV) that still today remains coarsely resolved below the surface and near the seafloor. Here, we gather evidence to confirm that Distributed Acoustic Sensing (DAS) technology can convert tens of kilometer-long seafloor fiber-optic telecommunication cables into dense arrays of temperature anomaly sensors having millikelvin (mK) sensitivity, thus allowing to monitor oceanic processes such as internal waves and upwelling with unprecedented detail. Notably, we report high-resolution observations of highly coherent near-inertial and super-inertial internal waves in the NW Mediterranean sea, offshore of Toulon, France, having spatial extents of a few kilometers and producing maximum thermal anomalies of more than 5 K at maximum absolute rates of more than 1 K/h. We validate our observations with in-situ oceanographic sensors and an alternative optical fiber sensing technology. Currently, DAS only provides temperature changes estimates, however practical solutions are outlined to obtain continuous absolute temperature measurements with DAS at the seafloor. Our observations grant key advantages to DAS over established temperature sensors, showing its transformative potential for the description of seafloor temperature fluctuations over an extended range of spatial and temporal scales, as well as for the understanding of the evolution of the ocean in a broad sense (e.g. physical and ecological). Diverse ocean-oriented fields could benefit from the potential applications of this fast-developing technology.