We went to Rome two years ago in August. For months prior to our trip I kept hearing people ask in disbelief that we were going to Italy and Spain in August. Well, I live in Washington, DC and the weather here in August is hot and humid. The weather in Italy and Spain was much more comfortable then DC in August.
As far as "Europe closes in August", don't believe it. We had a great time in Rome and in fact we stayed at the Rome Hilton Cav and it is an amazing hotel.