A sound-cancelling flow-through muffler includes a linear first inner passage, and a curved or zig-zagged second outer passage that wraps around or surrounds the inner passage and that is situated between the linear first inner passage and an exterior wall of the muffler. The outer passage has a length that is equal to, or a multiple of, one-half the wavelength of sound to be cancelled by the muffler such that sound exiting the inner and outer passages destructively interferes or cancels in a sound cancellation or conversion chamber. In addition, the walls of the outer passage serve as a heat sink to extract heat from the exhaust stream and conduct the heat to the outside of the housing. Alternatively, the outer passage may have a closed such that reflects sound back toward the inner passage for cancellation, the walls of the outer passage continuing to serve as a heat sink to extract heat from the exhaust stream and conduct the heat to the outside of the housing.