Lithium cobalt oxide is a convenient model material for the vast family of cathode materials with a layered structure and still retains some commercial perspectives for microbatteries and some other applications. In this work, we have used ab initio calculations, x-ray diffraction, Raman spectroscopy, and a theoretical physical model, based on quasi-harmonic approximation with anharmonic contributions of the three-phonon and four-phonon processes, to study a temperature-induced change of Raman spectra for LiCoO2. The obtained values of shift and broadening for Eg and A1g bands can be used for quantitative characterization of temperature change, for example, due to laser-induced heating during Raman spectra measurements. The theoretical analysis of the experimental results lets us conclude that Raman spectra changes for LiCoO2 can be explained by the combination of thermal expansion of the crystal lattice and phonon damping by anharmonic coupling with comparable contributions of the three-phonon and four-phonon processes. The obtained results can be further used to develop Raman-based quality control tools.