The solution is to use another browser (in my case Firefox) and set preferences to download files to a RAMdisk.
Make RAM Disk is a free application, and a few meg won't be missed from your system RAM. You'll probably want to load the RAMdisk at startup so put the application in your System Preferences » Account » Login Items.
I view the RAMdisk volume in List or Cover View and keep the Date Modified column highlighted. This way the last few downloads are easy to find. When you see a file you want to keep, move it to the relevant folder.
RAMdisk is volatile, so you don't need to clean it out. The contents magically disappear at your next system reboot.
[crarko adds: I tested this, and it still works as described in 10.6.6. I tend to be a packrat so I hang on to my downloaded files and then sort through them every few months. If you have very large downloads I'll also refer you to this previous hint, which describes a method to create a large RAMdisk if you have the memory to do it.]

