I see that there is a lot of input on this topic so I'm not going to check & see if anyone else suggests what I'm about to say.
Our boat has an older small A/C and we don't have a generator. We do have 600Ah of battery and 660W of Xantrex solar panels. But no soft start to use the A/C. So, running the A/C is not an option.
We also have a boat designed properly with a hatch on the fwd deckhouse over the V-berth and another aft on the sundeck over the aft MSR. After buying our boat I put truck sun reflector panels in the 3 fwd windows at the end of the deckhouse. You might be able to see what I am mentioning in my profile picture. IF NOT PM me.
To finish setting the stage we usually are on our boat doing the Loop from May/June to October/November and then put the boat up for the winter. This yr we are in FL sitting out hurricane season.
I don't think, per se that the heat is an issue but if you allow it to excape then it will be less of an issue. Most dog their boats down so no air can move and then compensate with humidifiers and A/C. Then further compensate with high water alarms and other alarms to keep an eye on the items that have been added.
We bought our boat in '10 and for the first 6yrs cruised the Chesapeake where she would be closed up for the work week.
We have never had mold or mildew and we don't run the A/C while we are away.
This winter we are in FL west of Okeechobee with no dock power available (old FL marina).
What I have done is install solar exhaust fans on the 2 hatches. Like these (
https://www.defender.com/product.jsp?path=-1|6880|2290139|2290144&id=3857882).
All you need to do is to keep air moving.
As said, I also added truck windshield sun reflectors in the 3 fwd windows can be obtained from Walmart, to keep the beating sun from getting into the boat.
We also have homemade hanging curtains that deflect the sun on all of the boat windows.
I have one of the solar fans pulling the air in and the other, pushing it out. I've even had the fans stop due to age or amount of sun available, yet the air circulation continues to work. It doesn't take much.
We're on 12yrs with our boat and never had mold or mildew.
Thought I'd throw our success out for others to know.