You can use your temporary directory, you can find it as an environment variable called TEMP, usually it'll be under C:\DWASFiles\Sites{sitename}\Temp.
One thing to note is that the maximum size allowed there is 500MB for free/shared sites (see documentation), for standard it's much higher (~200GB which is shared between sites in that instance).
Also maybe trivial but the temporary directory is temporary (will probably be removed when the site is recycled) and one instance cannot see another's temporary directory.