In the beginning of September, the average temperature usually is between 9°C and 17°C. Although you still may face showers, the weather in St. Petersburg is drier in September than it is in July and August. During this period it is unlikely to be very cold, but you might also want to pack a scarf, gloves, and a light waterproof jacket or umbrella.
Don’t worry too much about the weather – whatever happens, you’ll still have an amazing time. Particularly if you go early in the month, you are likely to have reasonably good weather, yet the attractions are quieter than they are in July and August!