Do wear light clothing
Do continually drink water ( sipping )
Do refresh yourself with an ice cream / Gelato
Blessed is the aircon especially when it's in the Vatican as well and of course the water is holy well it must be as the Pope lives there ;-)
You honestly can't cope in Rome without drinking copious amounts of water and filling up at the various little water fountains dotted here there and everywhere. The blue fountains in Rome are affectionately known as "Blue Noses"
Now in England I'm sure Gin fountains would catch on , I shall be writing to the Prime Minister with this very idea.