Three-dimensional carrier-phase Direct Numerical Simulations (DNS), combined with a Lagrangian representation of individual droplets, have been employed in this parametric study to examine the physical effects of liquid water mist interacting with laminar and turbulent premixed stoichiometric n-heptane air flames. Significant reductions of flame temperature and burning velocity have been observed in the presence of water droplets. In agreement with the laws governing evaporation, a strongly non-linear influence of the droplet size on the overall burning rate has been noted, whereas the influence of water loading is fairly linear. Different regimes of droplet-flame interaction are known to exist and this has been investigated by numerical experiments focusing on the influence of the latent heat of vaporization. When using realistic fluid properties of water, the cooling effect due to the enthalpy sink of evaporating droplets outweighs the dilution effect due to the local release of steam. Under turbulent conditions, the effectiveness of the droplets in reducing the overall burning rate changes owing to the transient nature of the droplet-flame interaction. Furthermore, it was found that the evaporating droplets significantly diminish the flame-generated turbulence and this leads to weaker turbulent wrinkling of the flame surface as compared to gaseous premixed reference simulations without droplets. Based on a comparison of the time scales representing droplet evaporation and the droplet residence time within the flame, a reduced-order model is proposed to account for both the cooling and dilution effects with respect to flame temperature and laminar burning velocity.