Miniaturized optical spectrometers providing broadband operation and fine resolution have an immense potential for applications in remote sensing, non-invasive medical diagnostics and astronomy. Indeed, optical spectrometers working in the mid-infrared spectral range have garnered a great interest for their singular capability to monitor the main absorption fingerprints of a wide range of chemical and biological substances. Fourier-transform spectrometers (FTS) are a particularly interesting solution for the on-chip integration due to their superior robustness against fabrication imperfections. However, the performance of current on-chip FTS implementations is limited by tradeoffs in bandwidth and resolution. Here, we propose a new FTS approach that gathers the advantages of spatial heterodyning and optical path tuning by thermo-optic effect to overcome this tradeoff. The high resolution is provided by spatial multiplexing among different interferometers with increasing imbalance length, while the broadband operation is enabled by fine tuning of the optical path delay in each interferometer harnessing the thermo-optic effect. Capitalizing on this concept, we experimentally demonstrate a mid-infrared SiGe FTS, with a resolution better than 15 cm-1 and a bandwidth of 603 cm-1 near 7.7 μm wavelength with a 10 MZI array. This is a resolution comparable to state-of-the-art on-chip mid-infrared spectrometers with a 4-fold bandwidth increase with a footprint divided by a factor two.