I looked again at your question and it looks to me like the problem is more a misuse of the "heredoc" rather than an open() question. A "heredoc" is often used say for a long bunch of text that you want to perhaps print or use in some other way. It is just a shorthand way of making a single string out of multi-line text.

print <<END;
This is some long winded window
text that could appear somewhere
and using this heredoc allows me to
type it in without having to double quote it
or put in "." concatenations or "\\n" characters
as this will be printed verbatim just like it is
except note that I had to double escape the newline!
Otherwise it would be a "newline"!
END
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So a "heredoc" just makes a string! There is no "open" involved, it is just a string like any other string. If you want to iterate over a number of constant values in your program, there are other ways:
1. Use @stuff like this: @stuff = qw (thing1 thing2 thing3);foreach (@stuff){..blah..}
2. For some test data, use a __DATA__ segment placed after your executable code. The DATA file handle doesn't need to opened or closed - you can just read from it.
I'm saying that putting a list of file names inside of a "heredoc" is a rather weird looking thing to do.

while (<DATA>)
{
   chomp;   #just to show you what the \n is there 
            #just like from a file..
   print "$_\n";
}
__DATA__
thing1
thing2
thing3
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There are a number of variations on open() which I think have been covered quite well below. I didn't know before that $somevar could be opened as a a RAM file (a memory resident temp file) in Perl 5.8. I've always just generated a "real" temp file in the past.

You cannot write to a "heredoc", nor to the DATA filehandle.