The SI unit of temperature. Spell out on first mention. Note the lower-case k (all SI units are lower case when spelled out); can be abbreviated to K (upper case) in subsequent mentions. Note that, although it is a measure of temperature, it is a standalone unit, not a type of degree, so never write "degrees kelvin" or "°K". The plural of kelvin is kelvins.

Kelvin is commonly used in scientific contexts, especially to talk about low temperatures. 1 K is equal to 1 °C in magnitude, but the starting points are different: 0 K = -273.15 °C (absolute zero).
In public-facing texts, it may be helpful to give the equivalent temperature in degrees celsius in brackets, e.g. The operating temperature of the LHC is 1.9 K (-271.3 °C).