Downloading big PDF files
Correctness

Files over 10240 bytes will fail to download because the streams are closed after one iteration of the while loop(Edit: Was paste error by OP). As of java 7, it is highly preferable to use a try-with-resources block when working with AutoCloseable objects.

Implementation

Wrapping your FileOutputStream in a BufferedOutputStream would be preferable to manually flushing.

Performance

You may see some performance gain by running each file download on its own thread. You'd need to take your existing code and move much of it into a Runnable or Callable. Use an Executor to perform some or all of the downloads concurrently.

If you made these modifications, the code might look more like:

import java.io.BufferedOutputStream;
import java.io.File;
import java.io.FileOutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.net.URL;
import java.net.URLConnection;
import java.util.Objects;
import java.util.concurrent.Callable;
import java.util.concurrent.ExecutorService;
import java.util.concurrent.Executors;

public final class FileDownloader {

    // or newFixedThreadPool() to control the number of threads.
    private final ExecutorService executor = Executors.newCachedThreadPool();

    public FileDownloader() {
        super();
    }

    public void downloadPdf(final URL targetUrl) throws IOException {
        final File destination = File.createTempFile("download-pdf-" + System.currentTimeMillis(), ".pdf");
        this.executor.submit(new DownloadCallable(targetUrl, destination));
    }

    private static final class DownloadCallable implements Callable&lt;File&gt; {

        private static final int BUFFER_SIZE = 1024 * 1024;

        private final URL targetUrl;
        private final File destination;

        public DownloadCallable(final URL targetUrl, final File destination) {
            this.targetUrl = targetUrl;
            Objects.requireNonNull(targetUrl);

            this.destination = destination;
            Objects.requireNonNull(destination);
        }

        @Override
        public File call() throws IOException {
            final URLConnection request = this.targetUrl.openConnection();
            try (final InputStream inputStream = request.getInputStream();
                    final FileOutputStream fileStream = new FileOutputStream(this.destination);
                    final BufferedOutputStream outputStream = new BufferedOutputStream(fileStream, BUFFER_SIZE);) {

                final byte[] data = new byte[10240];
                int bytesRead = 0;
                while ((bytesRead = inputStream.read(data)) != -1) {
                    outputStream.write(data, 0, bytesRead);
                }
            }
            return this.destination;
        }
    }
}