An RF cavity resonator that includes: a resonator chamber for containing an RF field; an RF coupling element coupled to the resonator chamber for introducing the RF field into and extracting the RF field from the resonator chamber; a tuning assembly for causing the RF field to resonate at a desired frequency, wherein at least a portion of the tuning assembly is coupled within the resonator chamber; and a heat transport element included in the tuning assembly for transporting heat from the RF cavity resonator, the heat transport element comprising a phase change material, a housing for enclosing the phase change material, means for circulating the phase change material within the housing, and an electrically conductive surface for isolating the phase change material from the RF field, wherein the phase change material undergoes a phase change during circulation within the housing.