# Untested. Note also that this code will not handle special
# cases as STDERR being closed, tied or attached to a file
# descriptor different than 2.

use autodie;
use File::Temp qw(tempfile);

open my $olderr, '>&STDERR'; # save STDERR
my $fh = tempfile();
open STDERR, '>&', $fh;

my $entry = Text::BibTeX::Entry->new($bib_entry);
open STDERR, '>&', $olderr; # flush and reset STDERR

seek($fh, 0, 0);
my $err = do { local $/; <$fh> };
close $fh;