. . . 
  $that_ref_to_his_sub = ...  # copied from your 
  $his_other_data_value = ... #   call to new()
  . . .
  while( $buffer = more_to_read() ) {
    if( defined $that_ref_to_his_sub ) {
      $bytes_read += length($buffer);
      &{$that_ref_to_his_sub}($filename,$buffer,$bytes_read,$his_other_data_value );
    }
    print $fh_tempfile $buffer;
  }
  . . .