Cut a 20″ length of 3/16″ x 3/4″ steel and punch a hole in one end the size of the rivets you want to heat. In the other end punch a hole for hanging this tool. Just put a rivet in the first hole and stick the rivet into your forge to heat. Lift it out when it’s hot, grab the rivet with tongs, and you’re ready to go. With just a little care you won’t lose any rivets in your coals or between your firebricks.
Make sure the two ends of this tool look noticeably different, so you’re less likely to pick it up by its hot end!