You'll be amazed how much info you lose when someday (might be tonight) your hard disk ("temporary storage" only) decides to go south, or some malware erases your data. You'll be glad than if you have a not too old backup on your laptop, or (better even) on a CD-RW. Having written it to CD-RW you can easily copy it to the backtop.

Moreover, you can use File>Export to export recent mails to a file while which you can import to your desktop to minimize the size of the file copied.

Hope this helps.