Laser-induced demagnetization is theoretically studied by explicitly taking into account interactions among electrons, spins, and lattice. Assuming that the demagnetization processes take place during the thermalization of the subsystems, the temperature dynamics is given by the energy transfer between the thermalized interacting baths. These energy transfers are accounted for explicitly through electron-magnon and electron-phonon interactions, which govern the demagnetization time scale. By properly treating the spin system in a self-consistent random phase approximation, we derive magnetization dynamic equations for a broad range of temperature. The dependence of demagnetization on the temperature and pumping laser intensity is calculated in detail. In particular, we show several salient features for understanding magnetization dynamics near the Curie temperature. While the critical slowdown in dynamics occurs, we find that an external magnetic field can restore the fast dynamics. We discuss the implication of the fast dynamics in the application of heat-assisted magnetic recording.