We present a photothermal spectroscopy setup based on a broadband mid-infrared quantum cascade laser frequency comb (QCL-FC). In this PTS detection scheme, local refractive index changes of the gas sample due to absorption-induced local temperature changes are detected optically by a near-infrared heterodyne interferometer. Until now, this method has been demonstrated only with single-frequency lasers in the mid-infrared region, which limits its capability of targeting broadband absorption features. The QCL-FC used in this work covers the spectral range from 7.7 to 8.2 µm with a repetition rate of 9.9 GHz. A Fourier transform spectrometer modulates the intensity of QCL-FC, which excites photothermal effect of the gas sample in a Herriott multipass cell with optical path of 76 m. Spectroscopic measurements on nitrous oxide is performed as proof of concept. This technique combines the sensitivity of PTS detection and the broadband mid-infrared coverage of QCL-FC, which has a great potential to further promote the applications of QCL-FC in trace gas sensing.