"'Berlin is beautiful in the summer. The weather is cool, not stifling like Italy.' Not necessarily, at least not these days. Maybe before Global Warming. I was in Berlin for six days in early August 2015, and it was hot--somewhere in the 80s."
Sure, but this is relative. We were in the Alsace the same summer, and while Northern Germany was in the low to mid 80's, Alsace hit 100+ every day. Our friends who choose Rome faced 107 at the height of the afternoon, cooling to the mid 90's by midnight. We eventual ate the sunk cost of our paid reservations and audibled to Northern Germany, where the 80's felt like delightful high-summer compared to the Death Valley heat farther south. Best $500 I've ever thrown away!
And that was a historic (literal unfortunately) killer heatwave. I wouldn't worry for a second about Berlin being too hot in August - it almost certainly won't be, and if it does heat up the city gets interesting - the clothes come off and the parks and massive swimming complexes come alive - culturally delightful experience to sit in the moderate heat at a shady beer garden near a riverbank full of Germans in uncharacteristic weather induced spreeish countenance.
I'd leave Italy for the delightful off-season and do Germany this time. When people say two cities is a lot for a week I feel the sentiment. But it can be done well. Here are a few guidelines:
Minimize transit times. From the US fly into a city you want to be in and fly out of a city you want to be in. If the two cities you want to visit are far apart fly between them. Fly or take a train very early in the morning or at night. Nothing wastes a day in a worse way than an 11am flight or non-scenic train ride. You wake up in the morning, wait around to leave, get in late enough that you drop your stuff and get some dinner and that's about it. Instead bite the bullet and make that 5am train or flight, or leave after 6pm. You could likely do 3 full days in Berlin and 3 full days in Copenhagen for instance by flying at efficient times.
Stick to one region and do some smaller places along with the large city. The biggest mistake first time Europe travelers make is ticking huge capitals off their list. That might make sense in the US, but Europe is so old and densely populated that the smaller cities are still quite sophisticated, not flavorless backwaters. They are relaxed and manageable. And villages even more so. For instance you could do Berlin, then Dresden or Leipzig, then Erfurt or some other little place. Renting a car for the "road trip" part of your regional trip gives you greater control over your schedule and you can be really efficient with your travel time.