{
  local $^W = 0;
  call_library_that_warns();
}

Rather than disabling all warnings as  local $^W = 0; does, it may be prudent to disable only the specific annoying warnings expected to be generated by the library in question. Consider

c:\@Work\Perl>perl -wMstrict -le
"sub foo {}
 my $u;
 ;;
 print 'before block';
 {
   print 'in block';
   sub foo {}
   print $u;
   my $r = substr 'x', 5, 5;
 }
 print 'still running after block';
"
Subroutine foo redefined at -e line 1.
before block
in block
Use of uninitialized value $u in print at -e line 1.

substr outside of string at -e line 1.
still running after block
[download]

versus

c:\@Work\Perl>perl -wMstrict -le
"sub foo {}
 my $u;
 ;;
 print 'before block';
 {
   print 'in block';
   no warnings qw(uninitialized  substr);
   sub foo {}
   print $u;
   my $r = substr 'x', 5, 5;
 }
 print 'still running after block';
"
Subroutine foo redefined at -e line 1.
before block
in block

still running after block
[download]

(Note that some warnings occur at compile-time, some at run-time.) See perllexwarn. (Update: With some version of Perl after 5.14.4, the content of perllexwarn was integrated into warnings; the former doc file is now a stub.)