We just did an almost identical trip -- 6 pm departure from ORD, through FRA, to Berlin. Of course, the ORD departure was delayed, so we got to veg out for a few hours in the LH SEN Lounge in FRA before getting to Berlin mid afternoon. Once we got to Berlin, however, we were able to walk around Mitte and to stay up til 10 pm Berlin time.

In addition to suggestions above, don't give up on the possibility of getting some sleep before FRA -- cut out caffeine at least 72 hours before your flight, DON'T drink alcohol on the plane, do consider a half-dose of Sonata or Ambien, put on earplugs or noise-cancelling headphones and the silly eyeshade, and plan an easy first day in Berlin ... drop your bags at the Marriott, even if you can't check in and then take a City Tour bus for a couple of hours, sit at the Starbucks at Pariser Platz by the Brandenburg Gate (or another coffeeshop along Unter den Linden), wander down Unter den Linden (or hop on a 100 bus) and sit in the Lustgarden if you are too tired to do a museum on MuseumInsel, sit in the Berliner Dom and read, etc. etc. The 100 bus from Pariser Platz down to Zoogarten is another lovely (cheap) ride, and then you're near Kadewe where you can have a snack (or at the outdoor market across the street). Don't feel you have to find a bed in order to slow your pace and rest!