Hot excitons are usually neglected in optical spectroscopy in 2D semiconductors for the sake of momentum conservation, as the majority of hot excitons are out of light cones. In this letter, we elaborate the contribution of hot excitons to optical properties of monolayer MoSe2 with photoluminescence (PL) and photoluminescence excitation (PLE) spectroscopy. With the excitation-intensity-dependent PL, temperature-dependent PL and PLE experiments combined with the simulations, we experimentally distinguish the influences of the exciton temperature and the lattice temperature in the PL spectrum. It is concluded that the acoustic phonon assisted photoluminescence accounts for the non-Lorentzian high energy tail in the PL spectrum and the hot exciton effect is significant to linear optical properties of TMDs. Besides, the effective exciton temperature is found to be several tens of Kelvin higher than the lattice temperature at non-resonant optical excitation. It indicates that the exciton temperature needs to be carefully taken into account when considering the exciton related quantum phase phenomena such as exciton condensation. It is experimentally demonstrated that the effective exciton temperature can be tuned by excitation energy.