A method for processing a part (10) with an energy beam A mask (70, 80) is arranged between a source of the energy beam and the part. The mask is configured with a beam-transmissive portion (71) in correspondence with mutually opposed portions (12, 14) of the part. Simultaneously heating the mutually opposed portions of the part is performed with energy beamlets passing through the beam-transmissive portions of the mask This simultaneous heating is configured to keep a thermally-induced distortion of the part within a predefined tolerance. Scanning of the mask with the energy beam may be performed without precisely tracking the mutually opposed portions of the part, thereby avoiding a need for complicated numerical programming for tracking a relatively complex geometry defined by the mutually opposed portions of the part.