An electrically controlled metamaterial perfect absorber (MPA) based on Mie resonance is demonstrated experimentally and modeled numerically. A ceramic dielectric cube is adhered to a specially shaped thin copper film sputtered on a quartz plate. By passing direct current (DC) through the film, the temperature of the cube can be varied, resulting in changing the cube's permittivity and shifting the absorption resonance frequency. The frequency increases on heating and the absorption is over 99% throughout the tuning range. This method for constructing miniaturized tunable MPAs compares favorably to bulky alternative designs. It also provides a versatile route to broaden the absorption bandwidth and potentially expand the range of applications such as metasurfaces and cloaking devices utilizing nonuniform permittivity absorbers produced by temperature gradients.