Where the weather in Italy is better and hotter: Rome, Pavia, Bari or Naples?

Think of it this way...the further South you go....the closer you are getting to the equator and Africa.

Hot enough yet?

However, having said that.........there will be places down South, but by the coast with decent breezes.........as opposed to cities like Rome or Naples, which will have staggering OPPRESSIVE Humidity, in the summer.........so, your idea of "Hot" may vary-

The Southern you go.. the hotter it is.

So, Bari.