A validated comprehensive axisymmetric numerical model, which includes the high pressure transient effects, variable thermo-physical properties and inert species solubility in the liquid phase, has been employed to study the evaporation of moving n-heptane droplets within a zero-gravity nitrogen environment, for a wide range of ambient pressures and initial freestream velocities. At the high ambient temperature considered (1000 K), the evaporation constant increases with the ambient pressure. At low ambient pressure, the evaporation constant becomes almost a constant during the end of the lifetime. At high ambient pressures, the transient behavior is present throughout the droplet lifetime. The final penetration distance of a moving droplet decreases exponentially with increasing ambient pressure. The average evaporation constant increases with ambient pressure. The variation is almost linear for reduced ambient pressures smaller than approximately 2. For higher values, depending on the initial freestream velocity, the average evaporation constant either becomes a constant (at low initial freestream velocities) or it non-linearly increases (at high initial freestream velocities) with the ambient pressure. Droplet lifetime decreases with increasing ambient pressure and/or increasing initial freestream velocity.