They were WRONG! Yes it is hot. And yes apparently most Italians are on vacation in August. But I'm sitting in my hotel room in Florence this morning and it's not even 8 and the city is buzzing. We have had no problems with restaurants or hotels being closed. A lot of monuments are under construction but those are 18 month or longer projects so it has nothing to do with summer.
Another thing is that people say "book ahead! It's the busy season." Well we didn't. We wanted to go where the wind blew us. Of course we had all our major destinations picked out and even a general time line but when we decided we had had enough of London we went to Paris early. So we booked our train just a couple days ahead and our hotels on the Travelocity app on the train to the next city (which has worked out great so far).
We live in Southern California so like I said the heat hasn't really been so bad. The humidity takes a couple days to get used to. Where sunscreen, bring a hat or buy one from one of the billion street vendors like I did. In Rome all the fountains are free drinking water so refill your bottles often. And in Paris and Florence we have had a couple nice rain showers to get a break from the heat. We even did Pompeii on a 90 degree day and it was alright. There is a lot of shade and more potable fountains.
Don't be discouraged about traveling to Europe in the summer!!