We present a detailed analysis of the far-IR properties of the bright, lensed, z = 2.3, SMG, SMM J2135-0102, using new observations with Herschel, SCUBA-2 and the VLA. These data allow us to constrain the galaxy's SED and show that it has an intrinsic rest-frame 8-1000um luminosity, L(bol), of (2.3 +/- 0.2) x 10^12 L(sun) and a likely SFR of ~400 M(sun)/yr. The galaxy sits on the far-IR/radio correlation for far-IR-selected galaxies. At ~>70um, the SED can be described adequately by dust components with T(d) ~ 30 and 60K. Using SPIRE's Fourier Transform Spectrometer we report a detection of the [CII] 158um cooling line. If the [CII], CO and far-IR continuum arise in photo-dissociation regions, we derive a characteristic gas density, n ~ 10^3 cm^-3, and a far-UV radiation field, G_0, 10^3x stronger than the Milky Way. L([CII])/L(bol) is significantly higher than in local ULIRGs but similar to the values found in local star-forming galaxies and starburst nuclei. This is consistent with SMM J2135-0102 being powered by starburst clumps distributed across ~2 kpc, evidence that SMGs are not simply scaled-up ULIRGs. Our results show that SPIRE's FTS has the ability to measure the redshifts of distant, obscured galaxies via the blind detection of atomic cooling lines, but it will not be competitive with ground-based CO-line searches. It will, however, allow detailed study of the integrated properties of high-redshift galaxies, as well as the chemistry of their ISM, once more suitably bright candidates have been found.