Split-pulse x-ray photon correlation spectroscopy using x-ray free-electron laser is a promising tool to probe atomic dynamics in liquid and soft-matter in picosecond time scale, which has been accessible only by spectroscopy. However, sample heating by x-ray beam is a major obstacle for this technique. Using molecular dynamics and the two-temperature model we examine the atomic level response of water to x-ray laser pulse at picosecond time scale and compare with observations from recent x-ray free-electron laser experiments. We investigate the effects of the heating due to x-ray laser pulses of different energies and the effects of the heat dissipation on the structure and dynamics of water through the atomic density correlation and the dynamic structure factor. Our results indicate, in agreement with experiment that in addition to the beam energy the time delay between the two pulses is a critical factor for obtaining reliable information on the atomic level dynamics of water.