Transient changes of the optical response of WS₂ monolayers are studied by femtosecond broadband pump-probe spectroscopy. Time-dependent absorption spectra are analyzed by tracking the line width broadening, bleaching, and energy shift of the main exciton resonance as a function of time delay after the excitation. Two main sources for the pump-induced changes of the optical response are identified. Specifically, we find an interplay between modifications induced by many-body interactions from photoexcited carriers and by the subsequent transfer of the excitation to the phonon system followed by cooling of the material through the heat transfer to the substrate.