Perhaps not a basic solution to a basic questions, but hopefully useful all the same

$SIG{__WARN__} = sub {
    open(ERR, ">>error.log") or die ("Died because: $!\n");
    print ERR @_;
    close(ERR);
};
[download]

What this does is re-assigns the __WARN__ signal handler (the thing that handles all warnings) to an anonymous sub that outputs the warnings to a file. So now STDERR should be nice and quiet.
HTH

broquaint