What kind of temperature unit is "cK"?
It actually is the common centi- prefix, but applied to temperature changes in units of Kelvins rather than absolute temperatures. The research as quoted by the Daily Mail obscures this by simplifying the results for a general audience.

The analyses and results are much more clearly described in the original refereed journal article, which clearly refers to changes in temperature - see in particular the discussion of their Fig. 1 (reproduced below), which explicitly refers to rates of temperature change of 0.1 and 0.02 °C at depths below 2000 m over the previous century, corresponding to cK contours of ~10 and near zero in the corresponding section of that figure.

So, the contours in the figure quoted by the Daily Mail represent changes in temperature between measurements made in the 1870s and the early 2000s, in units of 0.01 K (or equivalently, 0.01 °C).


Figure 1 from Gebbie and Huybers (2019), https://doi.org/10.1126/science.aar8413 - reproduced here for non-commercial use.