The answer is complicated and not a single number. The amount of thermal expansion for a given volume of ocean depends on depth (pressure), salinity, and temperature. That is, a 1C change from 10C to 11C will produce a different amount of expansion than 21C to 22C. What this means is that if you take a fixed quantity of energy (like, say, a gigajoule) and inject it as heat into different parts of the ocean, you will observe different amounts of thermal expansion. Thus, even an "average" warming of 1C across the entire ocean can manifest as a surprisingly wide range of thermal expansions, depending on the particular temperature deltas within each part of the ocean. That is, the final expansion will depend on the distribution of the thermal change.
The best we can do is build models which attempt to make reasonable inferences of the heat distribution and compare them to actual measurements taken by buoys, satellites, and other instruments. This is how the IPCC estimates the thermosteric component of mean sea level rise: https://www.nap.edu/read/13389/chapter/5. Some studies suggest that atmospheric-driven thermosteric expansion can be inferred down to 600m, while others suggest it penetrates further.
The EPA says that the average sea surface temperature (SST is a significant area of study all by itself) has increased on average about 0.07C/decade for the last century: https://www.epa.gov/climate-indicators/climate-change-indicators-sea-surface-temperature. Now, that probably doesn't sound like much change. Barely over half a degree for a whole century! But you need to consider that water has significantly higher density and specific heat than air, so the amount of energy it takes to warm a kg of air is much less than needed to warm a kg of ocean, let alone a m^3.
IPCC estimates conclude that the ocean has absorbed about 93% of the excess energy trapped during the last century or so: https://portals.iucn.org/library/sites/library/files/documents/2016-046_0.pdf. What this means is that 1C of atmospheric warming only corresponds to a small fraction of a degree of oceanic warming (hence, the 0.07C/decade).
Even so, thermal expansion is believed to account for at least half of all sea level rise in the last century or so. But to answer your question most directly, NASA documents that from 1970 or so, the ocean has risen about 5 mm/decade, with a corresponding ocean temperature increase of 0.015C/decade (note the different rates cited are due to vastly different timescales). This implies an observed ratio of about 333 mm/1C average ocean temperature increase in the top 700m of ocean. This is about 2x the rate given by @Ben51, and less than half given by @Anthony Herrera.