How can I serve a PDF to a browser without storing a file on the server side?

The people who advise you to use response.getOutputStream() instead of creating a FileOutputStream are right. See for instance the Hello Servlet from Chapter 9 of my book:

public class Hello extends HttpServlet {
    protected void doGet(HttpServletRequest request, HttpServletResponse response)
        throws ServletException, IOException {
        response.setContentType("application/pdf");
        try {
            // step 1
            Document document = new Document();
            // step 2
            PdfWriter.getInstance(document, response.getOutputStream());
            // step 3
            document.open();
            // step 4
            document.add(new Paragraph("Hello World"));
            document.add(new Paragraph(new Date().toString()));
            // step 5
            document.close();
        } catch (DocumentException de) {
            throw new IOException(de.getMessage());
        }
    }
}

However, some browsers experience problems when you send bytes directly like this. It’s safer to create the file in memory using a ByteArrayOutputStream and to tell the browser how many bytes it can expect in the content header:

public class PdfServlet extends HttpServlet {

    protected void service(HttpServletRequest request, HttpServletResponse response)
        throws ServletException, IOException {
        try {
            // Get the text that will be added to the PDF
            String text = request.getParameter("text");
            if (text == null || text.trim().length() == 0) {
                 text = "You didn't enter any text.";
            }
            // step 1
            Document document = new Document();
            // step 2
            ByteArrayOutputStream baos = new ByteArrayOutputStream();
            PdfWriter.getInstance(document, baos);
            // step 3
            document.open();
            // step 4
            document.add(new Paragraph(String.format(
                "You have submitted the following text using the %s method:",
                request.getMethod())));
            document.add(new Paragraph(text));
            // step 5
            document.close();

            // setting some response headers
            response.setHeader("Expires", "0");
            response.setHeader("Cache-Control",
                "must-revalidate, post-check=0, pre-check=0");
            response.setHeader("Pragma", "public");
            // setting the content type
            response.setContentType("application/pdf");
            // the contentlength
            response.setContentLength(baos.size());
            // write ByteArrayOutputStream to the ServletOutputStream
            OutputStream os = response.getOutputStream();
            baos.writeTo(os);
            os.flush();
            os.close();
        }
        catch(DocumentException e) {
            throw new IOException(e.getMessage());
        }
    }
}

For the full source code, see PdfServlet. You can try the code here: http://demo.itextsupport.com/book/