All the places you mention are likely to be experiencing the same weather as Rome on the day you are there. It may well be very hot. Rome gets a lot of tourists, but it is a large city. Most of the people you see out on the sidewalk will be Romans, not tourists. For me, the major issue with crowds is their impact on ticket lines at the major sights. If you're on a bus tour you may not be standing in such lines. If you arrange your own transportation to Rome, you have the choice of skipping places like the Colosseum where the lines are always long or trying to get your tickets in advance.
In addition, Rome has a lot of lovely churches. Old churches are usually pretty comfortable on hot days because of the their thick stone walls. At least a few of the museums are probably air conditioned, though many are not. I don't know whether that information is readily available online.
It will be easy to find gelato stands and places to buy bottles of cold water in any area with a lot of people out on the street, which includes anywhere you'd be likely to be in Rome on a day-trip. The question is: If you take a tour to Rome, will you have the flexibility to stop whenever you want for a cold drink or gelato? My guess is that you will not, and a one-day package tour to Rome would not be my choice.