Michael Heerdegen via "Bug reports for GNU Emacs, the Swiss army knife
of text editors" <bug-gnu-emacs@gnu.org> writes:

> #+begin_src emacs-lisp
> (progn
>   (set-transient-map (let ((m (make-sparse-keymap)))
>                        (define-key m [?^]
>                          (lambda () (interactive) (message "Hmm...")))
>                        m))
>   (let ((overriding-terminal-local-map nil))
>     (recursive-edit)))
> #+end_src

A possible approach that seems to fix the reported bug: