The temperature-dependence of the direct band gap and thermal expansion in the metastable anti-ReO3 semiconductor Cu3N are investigated between 4.2 and 300 K by Fourier-transform infrared spectroscopy and x-ray diffraction. Complementary refractive index spectra are determined by spectroscopic ellipsometry at 300K. A direct gap of 1.68eV is associated with the absorption onset at 300K, which strengthens continuously and reaches a magnitude of 3.5×105cm-1 at 2.7eV, suggesting potential for photovoltaic applications. Notably, the direct gap redshifts by just 24meV between 4.2 and 300K, giving an atypically small band-gap temperature coefficient dEg/dT of -0.082meV/K. Additionally, the band structure, dielectric function, phonon dispersion, linear expansion, and heat capacity are calculated using density functional theory; remarkable similarities between the experimental and calculated refractive index spectra support the accuracy of these calculations, which indicate beneficially low hole effective masses and potential negative thermal expansion below 50K. To assess the lattice expansion contribution to the band-gap temperature-dependence, a quasiharmonic model fit to the observed lattice contraction finds a monotonically decreasing linear expansion (descending past 10-6K-1 below 80K), while estimating the Debye temperature, lattice heat capacity, and Grüneisen parameter. Accounting for lattice and electron-phonon contributions to the observed band-gap evolution suggests average phonon energies that are qualitatively consistent with predicted maxima in the phonon density of states. As band-edge temperature-dependence has significant consequences for device performance, copper nitride should be well suited for applications that require a largely temperature-invariant band gap.