Firstly, check if the power indicator is flashing or not.
When the system is in a standby state (power indicator is flashing with reddish brown color), power is supplied to the computer and the fan sometimes keeps rotating to release the heat. This is the specification.
When the power is off, or the computer is in a hibernation state (power indicator is off), the fan stops.
This VAIO computer is designed to detect the heat inside and release it even when the system is not in operation.
Therefore, the fan will rotate at high speed right after turning the power on, or when resuming from the power saving mode. The fan will also sometimes keep on rotating even after the computer shifts into power saving mode. However, this is not a hardware defect.