Why interval conversion is different
Absolute temperature scales use different zero points. Celsius sets 0 at the freezing point of water, Fahrenheit uses a different historical zero, and Kelvin starts at absolute zero. When you convert a measured reading such as 20 °C into Fahrenheit or Kelvin, those offsets matter.
Temperature intervals work differently because they describe only the size of a change. If one process warms by 10 °C, the same process has also warmed by 10 K. The zero-point offset drops out because you are not translating the starting temperature itself, only the difference between two readings.