Strange, I have never had any problem telling firefox where to download anything. You do have enough free space before starting the download? (e.g. df -H ) any volume has less than say 85% then you might want to grow that volume a little first.
What you could try is to manually mount the USB volume on top of the Firefox tmp folder instead. Then that one directory will have that whole volume for that one temp directory/file.
Alternately you can Google how to create a temp file in dom0 with 'truncate', create a loop device for it, and pass that device into the AppVM, format the volume ext4, and mount it where you need that extra space temporarily. If you look up how to upgrade a fedora template you can find the general instructions there to use as an example, only where you mount it will be different.