An arrayed-waveguide grating multiplexer with thin-film heaters is fabricated to compensate for phase errors in arrayed waveguides. The phase errors are measured by Fourier transform spectroscopy with a low-coherence interferometer and are used as a monitor when we adjust the phases by controlling thin-film heaters. A channel crosstalk of -25dB and a loss of 4.2dB are achieved in a 5x5 10GHz-spaced multiplexer.