Weather

The science is pretty settled. But while we should all prepare for more weather fluctuations as a result, I still think your best bet is to look at one of the various weather sites and compare the past 2-3 years.

The science may be settled on the fact that temperatures are rising, and on the fact that rise is caused primarily by an increase in CO2 emissions in the atmosphere especially due to human activities, in particularly since the Industrial Revolution. The climate however has not changed in drastic ways yet. In the last 50 years the average temperatures in Rome have increased only about 1.5 degrees Celsius. That means that the average high temperature at the end of May is now about 25 degrees Celsius (77 F) instead of maybe 23.5 degrees C (74 F), 50 years ago. Rain precipitation has not registered a significant change since 1950, but end of May/June is generally drier than autumn or spring, so you don’t have to worry too much about rain, but have a pocket umbrella just in case for the occasional thunderstorm.
There is no way to know now what the weather will be at your destination in 6 weeks, but weather forecasts tend to be reliable about 7 to 10 days forward, so check any weather app just before you depart, and you should have a better idea of what to expect. One thing I could safely bet on, even now, is that in none of the cities you are visiting there will be snow.