We confirm the planetary nature of two gas giants discovered by the Transiting Exoplanet Survey Satellite to transit M dwarfs. TOI-3714 (V = 15.24, J = 11.74) is an M2 dwarf hosting a hot Jupiter (M_p = 0.70 ± 0.03 M_J and R_p = 1.01 ± 0.03 R_J) on an orbital period of 2.154849 ± 0.000001 days with a resolved white dwarf companion. TOI-3629 (V = 14.63, J = 11.42) is an M1 dwarf hosting a hot Jupiter (M_p = 0.26 ± 0.02 M_J and R_p =0.74 ± 0.02 R_J) on an orbital period of days. We characterize each transiting companion using a combination of ground-based and space-based photometry, speckle imaging, and high-precision velocimetry from the Habitable-zone Planet Finder and the NEID spectrographs. With the discovery of these two systems, there are now nine M dwarfs known to host transiting hot Jupiters. Among this population, TOI-3714 b (T_eq = 750 ± 20 K and TSM = 98 ± 7) and TOI-3629 b (T_eq = 690 ± 20 K and TSM = 80 ± 9) are warm gas giants amenable to additional characterization with transmission spectroscopy to probe atmospheric chemistry and, for TOI-3714, obliquity measurements to probe formation scenarios.