We present two techniques for mitigating the effects of temperature drifts in waveguide spatial heterodyne Fourier-transform on-chip spectrometers. In high-resolution devices, large optical path length differences result in an increased sensitivity to temperature variations and impose stringent requirements on the thermal stabilization system. In order to overcome this limitation, here we experimentally demonstrate two new temperature mitigation techniques based on a temperature-sensitive calibration and phase error correction. The spectrometer chip under analysis comprises an array of 32 Mach-Zehnder interferometers fabricated on a silicon-on-insulator platform. The optical path delays are implemented as microphotonic spirals of linearly increasing length up to 3.779 cm, yielding a spectral resolution of 17 pm. We demonstrate that the degradation in retrieved spectra caused by temperature drift is effectively eliminated by temperature-sensitive calibration and phase error correction.