You are putting new line characters back with your print inside the loop. The loop handles one line at a time - it doesn't slurp the whole file. Probably the best fix is to move the print of the newline to after the read loop:

open my $inData, '<', $tmpfile or die "Can't open $tmpfile: $!";
while (defined (my $data = <$inData>)) {
    chomp $data;
    print $data;
}
close $inData;

print "\n";
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Note the use of the three parameter version of open and the result checking using die. Note too the use of a lexical for the file handle and that you don't need to interpolate the file name into a string.

If you are assigning to a variable in the while loop condition you need to use defined to make the same test that Perl's magic while (<fh>) handling makes for you.

The chomp should be all you need to strip line separators, but watch out for OS differences in line endings (if that is an issue).