Yes, it has been a hot year but normally in the Med the temps will be in the mid 80s to low 90s in the coastal areas (such as the Greek Islands). Some inland places such as Rome do tend to get quite hot in the summer (we love hot weather). As to choosing a cruise...the OP needs to keep in mind that cruising in the Med is an entirely different experience then the Caribbean. In the Med the ports are king and onboard activities usually take a minor secondary role. In the evenings many passengers will go to bed relatively early since the long port days tend to wear-out many cruisers tend to cram in a lot in the ports.

Traveling with a 5 year old in Europe does mean that the OP needs to consider some compromise in the ports. For example, wheras many folks visiting the port of Naples for the first time will want to go to Pompeii...this is not always the best place to take a 5 year old if its a hot time of year. Personally, we think 5 is a tough age for Med cruises and we would probably suggest an itinerary that allows for some easy days (such as a beach day on a Greek Island). Although we traveled with our daugher when she was young we did not start dragging her around European cities until she was 9 and had enough endurance to handle the long days and lots of walking. At that age things were really well since we took frequent ice cream/gelato breaks and were able to plan some things that were of interest to a child. But the 3-7 age range has its own issues which require lots of thought about how to spend port days.