All units can be decomposed into the fundamental units of mass, length, and time. Some would also add the fundamental unit of charge, which used to be the coulomb but is now, I think, the ampere1.
For example, the watt is a joule per second; the joule is a newton-meter; the newton is a kilogram-meter squared per second squared2. You will have to do a similar decomposition of a Kelvin (or a degree Celsius or Fahrenheit).
1. The ampere was once defined as one coulomb per second. But now I think the coulomb is defined as an ampere-second.
2. The unit of force is the newton, F = ma, and the units for acceleration are meters per second squared.