More than 90% of the energy trapped on Earth by increasingly abundant greenhouse gases is absorbed by the ocean. Monitoring the resulting ocean warming remains a challenging sampling problem. To complement existing point measurements, we introduce a method that infers basin-scale deep-ocean temperature changes from the travel times of sound waves that are generated by repeating earthquakes. A first implementation of this seismic ocean thermometry constrains temperature anomalies averaged across a 3000-kilometer-long section in the equatorial East Indian Ocean with a standard error of 0.0060 kelvin. Between 2005 and 2016, we find temperature fluctuations on time scales of 12 months, 6 months, and similar to 10 days, and we infer a decadal warming trend that substantially exceeds previous estimates.