Overview: We (wife and I) rented this apartment with our relatives (parents, in-laws, and sister/brother-in-law) in June during July-like temperatures. No lift so be sure you can get to the 3rd floor (European 2nd floor) via stairs.
Positive(s): The location was wonderful and put us right in the middle of everything. 3 of the 4 showers had electric heaters which ensured hot water as well as good pressure (the 4th shower didn't have this and it was unusable; Frederick says he is planning to correct this). There were "central" AC's in each bedroom as well as the living room which was amazing. Frederick was one of the most genuinely nice people we have ever met and made sure that each question/minor snag was addressed quickly. Frederick also set us up with a massive amount of fruit, cookies, croissants, etc., upon arrival. The 2 washing machines were great as were the assortment of both adapters and converters.
Negative(s): The AC's is several rooms were weak and could not maintain a reasonable temperature (at least for us damn Americans). We killed several mosquitoes and spiders and had many bites (We DO NOT think this is due to the apartment but just due to Florence). Please understand that you're near the Duomo (as stated) which means you WILL hear the bells and the bustling tourists at night but the location may be worth it (it was to us).
Don't forget to buy one of Frederick's great paintings displayed at his art gallery nearby.