The behaviors of n-heptane droplet ignition in a high-temperature convective environment are studied numerically. Two cases are considered wherein one is a purely forced convection, and the other is a mixed convection. The ignition process can be divided into a heating-up evaporation, a nearly constant droplet temperature evaporation and a constant droplet-temperature burning. During the heating-up evaporation stage, the droplet temperature rises sharply and the square of the diameter decreases slightly with time. In the next stage, the droplet remains at nearly constant temperature in a pure vaporization process. After ignition, an envelope flame appears and the droplet is in an augmented vaporization process. The d2-law still holds. In the mixed convection case, where the gravity effect is taken into consideration, the location of initiation of chemical reaction is closer to the droplet, the ignition takes place earlier, and the flame is subjected to more stretch. The fuel accumulation phenomenon is also identified and it results in a suppression of the fuel evaporation rate. Finally, several future extensions are proposed to further modify the combustion model.