when you first start the cpu temperature is not more than 15 degrees, within 5 seconds after all the system will work raises the temperature rise of about 19c ~21C (i think ) and fan automatic right to work.
your fan do not need to spin if the temperature is very cold, and you can check in bios that your settings on auto, and it seemed normal for a computer all, some time we can found it int the software Fan roll in 0 speed.