use Fcntl qw(F_SETFD F_GETFD FD_CLOEXEC);

my $ssherr = File::Temp->new;
my $flags = fcntl($ssherr, F_GETFD, 0)
    or die "Can't get FD flags for '$ssherr': $!";
fcntl($ssh_err, F_SETFD, $flags & ~FD_CLOEXEC)
    or die "Cant clear close-on-exec flag for '$ssherr': $!";

<the rest of your code>