In a recent $paper^1$ we reported equilibrium (EMD) and non-equilibrium (NEMD) molecular dynamics simulations of liquid argon using the Green-Kubo relations and NEMD algorithms to calculate the thermal transport coefficients-the self-diffusion coefficient, shear viscosity, and thermal conductivity. The overall agreement with experimental data is quite good. In this paper the same technique is applied to calculate the thermal transport coefficients of liquid water at 298.15 K and 1 atm using TIP4P model for the interaction between water molecules. The EMD results show difficulty to apply the Green-Kubo relations since the time-correlation functions of liquid water are oscillating and not decaying rapidly enough except the velocity auto-correlation function. The NEMD results are found to be within approximately ${pm}$30-40% error bars, which makes it possible to apply the NEMD technique to other molecular liquids.