Imperfect cavity mirrors in the arms of an interferometric gravitational-wave (GW) detector can result in the generation of unwanted higher order modes that are close to or at resonance in the cavity. This can lead to many undesirable effects such as increased round-trip losses or degraded contrast defect. Polishing mirrors to fulfill the requirements of 2nd generation GW interferometers is extremely challenging. For the use of LG33 modes in 3rd generation detectors it would be necessary to improve polishing by an order of magnitude. In this article we present a novel technique for the in situ correction of cavity mirror surface figures by central heating residual aberration correction. This system targets and corrects specific features of the mirror surface figure such as to reduce scattering from the fundamental cavity mode to specific higher order modes by more than an order of magnitude. We demonstrate, by simulation, the feasibility of such a system and give examples of its application to 2nd and 3rd generation GW interferometers.