Broad-line radio galaxies (BLRGs) are active galactic nuclei that produce powerful, large-scale radio jets, but appear as Seyfert 1 galaxies in their optical spectra. In the X-ray band, BLRGs also appear like Seyfert galaxies, but with flatter spectra and weaker reflection features. One explanation for these properties is that the X-ray continuum is diluted by emission from the jet. Here, we present two NuSTAR observations of the BLRG 3C 382 that show clear evidence that the continuum of this source is dominated by thermal Comptonization, as in Seyfert 1 galaxies. The two observations were separated by over a year and found 3C 382 in different states separated by a factor of 1.7 in flux. The lower flux spectrum has a photon-index of Γ = 1.68 +0.03 −0.02 , while the photon-index of the higher flux spectrum is Γ = 1.78 +0.02 −0.03 . Thermal and anisotropic Comptonization models provide an excellent fit to both spectra and show that the coronal plasma cooled from kT e = 330 ± 30 keV in the low flux data to 231 +50 −88 keV in the high flux observation. This cooling behavior is typical of Comptonizing corona in Seyfert galaxies and is distinct from the variations observed in jet-dominated sources. In the high flux observation, simultaneous Swift data are leveraged to obtain a broadband spectral energy distribution and indicates that the corona intercepts ∼ 10% of the optical and ultraviolet emitting accretion disk. 3C 382 exhibits very weak reflection features, with no detectable relativistic Fe Kα line, that may be best explained by an outflowing corona combined with an ionized inner accretion disk.