In figure "Listing 3" of this paper, the author presented a recommended C code for creating secure temporary files. If that code is modified to the following one, is it still secure? Why or why not?

        char *filename;
        FILE *fp;
        do {
          filename = tempnam (NULL, "foo");
          fp = fopen (filename, "w");
          free (filename);
        } while (fp == NULL);