The oceans are absorbing much of the heat from climate change.
How is all of this heat measured?
The easiest way this is measured is via Argo floats. They're probes which periodically dive into the sea, and measure the ocean heat content.
This is done by calculating the formula. According to the European Environmental Agency, this formula is:
Ocean heat content is defined as the integrated temperature change times the density of seawater, times specific heat capacity from the surface down to the deep ocean.
This could also be done manually by calcuating out the formula, and obtaining the temperature of the seawater by using a device such as a Nansen Bottle.
Most of the heat balance calculations in the ocean use satellite-measured sea surface temperature (SST). This provides global temperature fields with daily variations. The interior heat content is determined using ARGO floats (as mentioned before), long-term mooring arrays (e.g., TAO, PIRATA) and extensive field cruises (e.g., WOCE) that use CTDs to measure temperature down to several thousand meters deep. Very few people use bottle samples (e.g., Nansen or Niskin bottles) for heat content estimates (they are used for sensor calibration for instance).
Ocean acoustic tomography is another method that can be used to measure temperature of large bodies of water, based on the speed of sound in water. Repeated measurements would therefore be able to show changes in ocean temperature. From the Wikipedia page:
A 1 °C change in temperature corresponds to about 4 m/s change in sound speed. An oceanographic experiment employing tomography typically uses several source-receiver pairs in a moored array that measures an area of ocean
This type of experiment would make use of a SOFAR channel, which acts as a waveguide for acoustic waves, allowing energy from a single source to travel large distances.