If you know some phrase or uncommon word from your file, you can search the raw sectors of the hard drive for pieces of text. This will turn up the text anywhere it might have been written: as paged out virtual memory, as a stil-existant file (temp file or saved file), or as temporary or saved file that was deleted and the space has not yet been rewritten.
But it will be slow. And if the file was never written to disk, it will yield nothing. And what it yields may be fragmented or incomplete.
Boot a Knoppix CD and start grepping! Knoppix is a linux installation that runs from CD, without writing to your hard drive.
If you have SCSI or SATA disks, you need to use /dev/sda
instead of /dev/hda
The other answer is correct, every moment that OS continues running decreases your recovery chances. pull the power and use another computer to prepare the knoppix CD.