Hello.

This usability issue is hopefully going to be addressed in Firefox 4. In the meantime, you can go into Tools > Options > Privacy > Firefox will:Use custom settings for history and untick Remember download history. Hopefully that's all you need?

In any case, downloads will still be stored in your computer if you don't delete them. Download history is independent from the actual downloaded files, so please be mindful of that.

With all due respect to my colleague Morbus, the way I read the OP's request is that he wants to automatically delete the actual file that he downloaded through Firefox when he closes Firefox, while retaining the download history of those files. That is diametrically opposed to how Firefox has always worked, and I haven't seen any mention of Firefox 4.0 having a new feature such as that.

BTW, 'autocomplete' data like "form and search history" is stored in a different file than "download history" data is stored,and there are separate preferences for toggling the saving of each (Options > Privacy) and the deleting of each in Clear Recent History./