use File::Copy;
use Getopt::Std;
use IO::Handle;
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Get Devel::Trace and try  perl -d:Trace -e ' require File::Temp; ' and try to find where it hangs

I think I nailed down the problem's cause. A simpler test case is

perl -e 'use Cwd; print getcwd'
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At some point this issues the following Cygwin calls

  168 4607616 main perl 9268 mount_info::conv_to_win32_path: src_path //Cwd.dll, dst \\Cwd.dll, flags 0x2, rc 0
  170 4607786 main perl 9268 build_fh_pc: fh 0x61276450, dev 000000C2
  937 4608723 WNetOpenEnum perl 9268 cygthread::stub: thread 'WNetOpenEnum', id 0x1A58, stack_ptr 0x109AD40
--- Process 9268, exception 000006ba at 767DC41F
2273000 6881723 main perl 9268 __set_errno: int stat_worker(path_conv&, stat*):1880 setting errno 2

Note that //Cwd.dll is interpreted as a network path on Windows and that WNetOpenEnum takes two seconds to execute, before failing with an exception. Tracing the code gives

$ perl -d:Trace -e 'use Cwd; print getcwd'
>> -e:1: use Cwd; print getcwd
>> /usr/lib/perl5/5.14/i686-cygwin-threads-64int/Cwd.pm:406:   *cwd = sub { &$orig_cwd() }

and this seems to be related to the following code.

if ($^O eq 'cygwin') {
  # We need to make sure cwd() is called with no args, because it's
  # got an arg-less prototype and will die if args are present.
  local $^W = 0;
  my $orig_cwd = \&cwd;
  *cwd = sub { &$orig_cwd() }
}