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Precision laser spectroscopy is key to many developments in atomic and molecular physics and the advancement of related technologies such as atomic clocks and sensors. However, in important spectroscopic scenarios, such as astronomy and remote sensing, the light is of thermal origin, and interferometric or diffractive spectrometers typically replace laser spectroscopy. In this work, we employ laser-based heterodyne radiometry to measure incoherent light sources in the near-infrared and introduce techniques for absolute frequency calibration with a laser frequency comb. Measuring the solar continuum, we obtain a signal-to-noise ratio that matches the fundamental quantum-limited prediction given by the thermal photon distribution and our system’s efficiency, bandwidth, and averaging time. With resolving power$R\sim <\#comment/>{10}^6$, we determine the center frequency of an iron line in the solar spectrum to sub-MHz absolute frequency uncertainty in under 10 min, a fractional precision 1/4000 the linewidth. Additionally, we propose concepts that take advantage of refractive beam shaping to decrease the effects of pointing instabilities by$100\times <\#comment/>$, and of frequency comb multiplexing to increase data acquisition rates and spectral bandwidths by comparable factors. Taken together, our work brings the power of telecommunications photonics and the precision of frequency comb metrology to laser heterodyne radiometry, with implications for solar and astronomical spectroscopy, remote sensing, and precise Doppler velocimetry.