The molecular process of heat conduction is studied with the molecular dynamics method for Lennard-Jones potential solid atoms. The probability density of the heat flux and its two-point time and space correlations are investigated for an understanding of the transfer mechanism of heat energy on the molecular level. The heat flux in the direction of the temperature gradient has a larger probability for carrying the molecular energy toward the low-temperature side than that toward the high-temperature side. The spatial length of the heat flux correlation is about 4 or 5 times the lattice length. Lattice defects in the solid reduce the correlation of heat flux, whereas lattice particles having deeper potential wells yield a stronger correlation of heat fluxes.