This paper presents simulations of the dynamics of nanosecond repetitively pulsed discharges between two point electrodes in atmospheric pressure air at 300 and 1000 K. At 300 K, the preionization left by successive discharges at the end of interpulses mainly consists of positive and negative ions with a density of about 10^9 cm−3 for a repetition frequency of 10 kHz. When photoionization is taken into account with a level of seed charges of about 10^9 cm−3, the dynamics and the characteristics of the discharge during a voltage pulse are shown to depend only weakly on the nature of negative seed charges (electrons or ions). At 1000 K, the preionization left by successive discharges at the end of interpulses consists of positive and negative ions and electrons with a density of about 10^10 cm−3 for a repetition frequency of 10 kHz. Simulation results show that the dynamics and the characteristics of the discharge during a voltage pulse remain rather close whatever the preionization level considered in the range 10^9-10^11 cm−3, corresponding to nanosecond repetitively pulsed discharges in the frequency range 1-100 kHz. The simulation of several consecutive nanosecond voltage pulses at a frequency of 10 kHz shows that, at 1000 K, the discharge can reach in a few voltage pulses a stable 'quasi-periodic' glow regime in agreement with experiments. Finally, the influence of an external air flow aligned with the electrode axis on the conditions to obtain a stable 'quasi-periodic' glow regime is discussed.