Question:
Why does inductor core saturation depend on the temperature?
Answer in 5 words:
In general, permeability is not a constant, as it can vary with the position in the medium, the frequency of the applied magnetic field, humidity, temperature, and other parameters.
Temperature Coefficient Of Magnetic Permeability from: NIST Research Library archive
Corelation of magnetic field and current, Ampere's law: B = f(u * I)