We investigated the spectral-dependent dielectric function and temperature-dependent bandgap energy of layered chalcogenide FeIn2Se4 crystals. The critical-point energy and Lorentzian broadening were analyzed by fitting second-derivative spectra using the standard critical point model. The temperature effect of the bandgap energy was analyzed based on an analytical model considering both thermal lattice expansion and electron-phonon interactions. We also extensively analyzed the temperature dependence of absorption tails and identified their possible origins. The dielectric functions and absorption coefficient in the photon-energy range of 0.75-4.75 eV were obtained. The results also showed that optical phonon modes associated with the electron-phonon interactions could be closely related to the average phonon energy.