Miniaturized integrated spectrometers will have unprecedented impact on applications ranging from unmanned aerial vehicles to mobile phones, and silicon photonics promises to deliver compact, cost-effective devices. Mirroring its ubiquitous free-space counterpart, a silicon photonics-based Fourier transform spectrometer (Si-FTS) can bring broadband operation and fine resolution to the chip scale. Here we present the modeling and experimental demonstration of a thermally tuned Si-FTS accounting for dispersion, thermo-optic non-linearity, and thermal expansion. We show how these effects modify the relation between the spectrum and interferogram of a light source and we develop a quantitative correction procedure through calibration with a tunable laser. We retrieve a broadband spectrum (7 THz around 193.4 THz with 0.38-THz resolution consuming 2.5 W per heater) and demonstrate the Si-FTS resilience to fabrication variations-a major advantage for large-scale manufacturing. Providing design flexibility and robustness, the Si-FTS is poised to become a fundamental building block for on-chip spectroscopy.