Sorry, can you elaborate and explain how this is related?
As far as I understand, we have a PID value for temperature (regardless of Celsius or Kelvin)
And we transition from one value to another, depending on the target temperature.
In other words, regardless of adding or removing the 273.15 conversion value, the behaviour would be exactly the same.
In Charles Law, wikipedia entry linked above, Volume of an ideal gas is linearly related to absolute temperature in Kelvin. I suspect that PID varying as a function of temperature is more likely to be linear using Kelvin rather than centigrade. I have not done actual PID calculations as a function of temperature but it would be consistent with how temperature impacts pressures and volumes.