For those not familiar with Stand-By mode, this means that you are putting your computer into a low-power state, but keeping some components still running. This allows you to save power, while still being able to start your computer a bit faster than if it had to start “cold”. This particular user was putting their computer into stand-by and heard noises coming from his computer even after the machine powered down.
The fan on your computer may indeed still run when your computer is in stand-by mode. This is because the computer itself is really still running while in stand-by and the CPU fan may run to keep your chip cool. There may be a setting in the BIOS (your computer’s hardware setup program) that can control this feature. You can access the BIOS when your computer first boots up usually by hitting the DEL or F2 key. That being said, if you are not familiar with the BIOS, you should be very careful if you choose to modify settings here as changing the wrong one could cause your computer not to start properly anymore.