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We demonstrate a broadband photothermal spectroscopy in the mid-infrared region using a quantum cascade laser frequency comb operating between ∼7.7 and ∼8.2 µm covering a frequency range of ∼70 cm^-1. The photothermal spectroscopy technique employs a Mach-Zehnder interferometer operating in a pump-probe configuration, where the mid-infrared pump beam is modulated by a Fourier transform spectrometer. A 76-m Herriott-type multipass cell is used for signal enhancement. As a proof-of-concept, we have measured the photothermal spectra of nitrous oxide that show good agreement with the HITRAN database. A minimum detection limit of 83 ppb of nitrous oxide in nitrogen is estimated from a broadband photothermal spectrum with 9.9 GHz spectral point spacing and acquired over 78 minutes. This detection scheme also provides over three orders of magnitude of photothermal signal linearity with gas concentration. This spectroscopic method combines the functionality of high sensitivity and background-free detection of photothermal spectroscopy as well as broadband mid-infrared operation of quantum cascade laser frequency comb, which could find applications in trace gas sensing systems that benefit from these features.