Barium Strontium Titanate tunability as a function of applied power

BaSrTiO is a high-permittivity material.
Thinking of its changes due to applying power means only heating it.
And yes, BaSrTio is highly temperature variable.
I would not name it "tuning"- by heating a material with RF power, it rather absorbs it.
BaSrTiO material is capable to vary its permittivity due to applied voltage, not power. Capacitors made of this material can be made to vary their capacitance by applied DC voltage.