I have spent many summers in Rome.
Prague is a toss up. Could be nice or could have a heat wave. who knows.
Rome on the other hand is consistently hot and humid in the summer.
I think Rome is an amazing city any time of the year.
Recommendations:

Do most of the walking earlier in the morning or in the evening/night.
Hotel must have air condition (which yours has)
Would be nice to have a pool to cool off in the afternoon.
Plan on taking taxis if you need to criss cross the city.
Maybe spend half a day at the beach. Still hot but breezier.
Would spend some time in the Borghese Park. Lots of trees with great shade.
Bring sunscreen protection and a hat.
If the travelers have medical problems, check with your doctor. Older travelers should be more careful about dehydration. They may not sense dehydration as well as younger people.
And yes, tap water in Rome is arguably the best in the world but in restaurants you get a dirty look when you ask for tap water. "We serve only bottled water"....

Are you crazy? Definitely not.
Enjoy