The third-generation wide bandgap semiconductor GaN currently occupies a hot spot in the fields of high-power electronics and optoelectronics. Fully exploring its optical and optoelectronic characteristics is of great significance. Here, we provide a systematic study on the temperature-dependent dielectric functions of GaN grown by metal-organic chemical vapor deposition in the spectral range of 0.73-5.90 eV via spectroscopic ellipsometry experiments and first-principles calculations. Ellipsometric measurements identify two typical absorption peaks that originate from the excitonic and phonon-assisted indirect absorption process, respectively. To explore the underlying physics, we perform first-principles calculations using the independent-particle approximation, model Bethe-Salpeter equation (mBSE), and phonon-assisted indirect absorption process (Inabs). In comparison with ellipsometric measurements, the mBSE calculation determines the absorption peak contributed by the many-body excitonic effect, while the Inabs calculation successfully predicts the second absorption peak. When heating the crystal, it observes the redshift and weakening of absorption peaks, intrinsically due to the nontrivial electron-phonon interaction as lattice vibration strengthens. While doping GaN with Fe or Si elements, the introduced free carriers modify the electronic interband transition. As the temperature increases, more free carriers are excited, and the temperature influence on the absorption peak is more significant than that of the undoped one. This work fully explores the physical origins of the temperature and doping effect on UV-Vis dielectric functions of GaN, aiming to promote its application in the fields of high-power electronic devices.