I believe this is a common issue with this specific model
Having googled it there are some solutions that you may want to try out
Do a search on this forum + google and you should find lots of assistance
I have seen a post by a couple other forum members and have posted one of these below
Hope this helps and let us know how you get on
VPCF13M1E/H fan noise.
The VPCF11 series had this problem which was addressed by a BIOS Update but I would expect this to have been fixed on newer models.
It may be that processes are running in the background that would cause the fan to provide more cooling - something like the Windows Indexing Service will run for some time with a new Vaio as it indexes the search of the hard drive. Have a look in Task Manager -> Performance to see if the CPU is working on a background process when the fan increases speed.
There is a 'How to troubleshoot fan noise' on the support pages for your model but it may not be the help you need:
http://genesis.sony-europe.com/instranet/ccil_sony/selfservice/search.jsp?DocId=29726&l=en_GB&m=VPCF...
If you believe the fan noise is excessive then I would contact Vaio Support and ask their advice.
