If we have not done so the day before, we should grasp the chance and climb Biberkopf as a first action today. It involves a short scrambling part (UIAA I) just before the peak. From there we can head on along the ridge and pay a visit to Hochrappenkopf and Rappenseekopf before we descend to Rappenseehütte again.
Now that we are warm, the main part of today's tour starts: Heilbronner Weg, which is a high-altitude crossing along the ridgeline of Hohes Licht ridge. Before the crossing we turn to the right to ascend Hohes Licht, which is the highest mountain of the ridge with 2651 m. The crossing itself is not super technical, but might be crowded and care needs to be taken anyway as we're constantly above 2500 m altitude, there's no fast way to leave the track and we're in terrain with high exposure. I.e. this is absolutely nothing for beginners. A last highlight of today is the ascent of Mädelegabel at the end of Heilbronner Weg. This is a slightly more technical ascent (UIAA I+). Daring and fit climbers might also decide to cross Hochfrottspitze towards Mädelegabel (UIAA III). Once back at the foot of the peak, it's a comfortable hike towards Kemptner Hütte. Expect the hut to be crowded by the way because it's also the first stop of E5, i.e. the Alp crossing Oberstdorf - Meran.