Nerdy browser question

When downloading a file that has an identical name to a file you've previously downloaded, is there any way to make Firefox automatically rename the downloaded file by, for example, appending a number, like Safari does?

To give you an example: I frequently save copies of satellite images from this NOAA site. These images have standard filenames -- for instance, the visible satellite photos are always called "vis.jpg." In Safari, when I click "Save image to [my downloads folder]" on one of these files, Safari automatically appends a number to the newly downloaded file's name. So, if you look in my downloads folder, you'll see "vis-1.jpg," "vis-2.jpg," "vis-3.jpg," etc., etc. This way, the old file isn't overwritten, and yet I'm not harassed with a window demanding that I create a new filename whenever I download this sort of file.

Firefox, on the other hand, always asks me for a filename when I click "Save Image As...", and if I stick with the default name -- the file's name on the Web -- it asks me if I want to replace the previously downloaded file with the same name. My options are "Cancel" or "Replace"; there is no "Automatically Rename" option. So, whenever I download a weather file with a standard name, I have to come up with a new and different filename each time. Given how often I download these sorts of files -- often several all at once -- this is an annoying waste of time. I want to just download it and have the naming take care of itself.

I find Safari's download method incredibly convenient to the point of indispensability, and it's really the only thing keeping me from switching to Firefox as my standard browser. So I was wondering if there might be some plugin or setting or whatever that would fix this.