In Mathematica, it is possible to reuse the output of the previous command by using %.
Is something similar possible for bash (or some other shell)?
For example,
If you use tee to duplicate the output stream to /dev/stderr, there's no need for a temp file; plus, after that, you can filter the stdout stream with sed to create a make_warning.log file - all in one line of Unix shell pipes.
make 2>&1 | tee /dev/stderr | \
sed -E -n 's/(.*[Ww][Aa][Rr][Nn][Ii][Nn][Gg].*)/\1/p' > make_warning.log