How to download a large file with the iPhone SDK and avoid memory usage issues?

I'm using the NSURLConnection class to download a large file in my iPhone application, but it crashes every so often because it's using too much memory. I'm doing the usual NSURLConnection usage, to append the received data to a NSMutableData object.

- (void)connection:(NSURLConnection *)connection didReceiveData:(NSData *)data {
    [self.fileData appendData:data];
}

Then after I finish downloading the whole file, I save it to a local temporary file, and read it as a mapped file like this:

- (void)connectionDidFinishLoading:(NSURLConnection *)connection {
    // save the downloaded data into a temporary file
    NSString *tempPath = NSTemporaryDirectory();
    NSString *tempFile = [tempPath stringByAppendingPathComponent:@"temp.pdf"];
    [self.fileData writeToFile:tempFile atomically:YES];
    NSData *mappedData = [NSData dataWithContentsOfMappedFile:tempFile];

    NSURL *baseURL = [NSURL URLWithString:@"http://mydomain.com"];
    [webView loadData:mappedData MIMEType:@"application/pdf" textEncodingName:@"UTF-8" baseURL:baseURL];
}

What can I improve here to avoid these memory usage problems?