Having something like ~/.cache as a tmpfs, and setting up xsession-errors to be there.
Of course, everything will be lost in the next reboot, and, depending on for how long the session goes, it may be too big for the set-up tmpfs space as well, for the people who use their PCs on a never-really-turn-off/reboot kind of regimen.
If one needs eventually something saved from session to session, maybe one can have a daemon that will tail/pipe the xsession-errors to some...