We present a new apparatus for active compensation of wavefront aberrations by controllable heating of a lens using a film heater matrix. The annular electric film heater matrix, comprising 24 individual heaters, is attached to the periphery of a lens. Utilizing the linear superposition, and wavefront change proportional to the heating energy properties induced by heating, a controllable wavefront can be defined by solving a linear function. The two properties of wavefront change of a lens have been confirmed through a specially designed experiment. The feasibility of the compensation method is validated by compensating the wavefront of a plate lens. The results show that the wavefront of the lens changes from 12.52 to 2.95 nm rms after compensation. With a more precise electric controlling board, better results could be achieved.