Phase-change materials (PCMs) have great potential in applications for data storage, optical switching and tunable photonic devices. However, heating the whole of the phase change material at a high speed presents a key challenge. Here, for the first time, we model the incorporation of the phase-change material (Ge2Sb2Te5) within a metamaterial perfect absorber (MMPA) and show that the temperature of amorphous Ge2Sb2Te5 can be raised from room temperature to > 900K (melting point of Ge2Sb2Te5) in just a few nanoseconds with a low light intensity of 150 W/m2, owing to the enhanced light absorption through strong plasmonic resonances in the absorber. Our structure is composed of an array of thin gold (Au) squares separated from a continuous Au film by a Ge2Sb2Te5 layer. A Finite Element Method photothermal model is used to study the temporal variation of temperature in the Ge2Sb2Te5 layer. It is also shown that an absorber with a widely tunable spectrum can be obtained by switching between the amorphous and crystalline states of Ge2Sb2Te5. The study lowers the power requirements for photonic devices based on a thermal phase change and paves the way for the realization of ultrafast photothermally tunable photonic devices.