Could the actual location be made adjustable, with the system-dependent defaults suggested as e.g., in comment #2 ? Maybe through an environment setting or a system-wide pref in share/octave/site/m/startup/

BTW, I'd second %LOCALAPPATA% on Windows systems (as %APPDATA% isn't meant for large(r) files cf. the specs in:
https://docs.microsoft.com/en-us/windows/uwp/design/app-settings/store-and-retrieve-app-data )
(although admittedly my own roaming profile at work is several 100s of MBs and on this home PC it is >700 MB.)

What would the optimal location on Mac OSX be?

Full agree. Would this only apply to '-forge' installs, or to any install that looks like a URL? Should also be a way to bypass or clear the cache?

On GNU/Linux, macOS, and Unix systems: ${XDG_CACHE_HOME:-~/.cache}/octave/...

On Windows: %LOCALAPPDATA%\octave\cache\...

This is based on the QStandardPaths::CacheLocation cross-platform logic.

It would be nice if pkg would cache its downloaded files somewhere.

This would speed up downloads for users on slow internet connections.

And as a minor GUI improvement, it would get rid of the temporary files flying in and out of the "Current Directory" display when you do a `pkg -forge` installation.

Somewhere under $XDG_CACHE_HOME, like `$XDG_CACHE_HOME/octave/pkg/downloads` would be an appropriate place on Unix. Somewhere under %LOCALAPPDATA% on Windows.

Low priority.