We report on the exponential decay of the red-shift of the photoluminescence A-exciton peak in monolayer molybdenum disulfide (MoS2) with the excitation laser power. The linear relationship found for the thermal variation of the same peak suggests that the laser power effect goes beyond the exciton dynamics associated to temperature variations. Laser exitation power effect on the broadening and red-shifting of the A(1g) and E(2g)1 phonon peaks observed by Raman spectroscopy reflect the damping of vibration due local thermal heating induced by the laser. Our results point out the laser excitation power dependence on the photoluminescence properties of monolayer MoS2.