My previous boat was like that.
We had a fan that blew across the port above the bed
to suck in fresh air and then blow it down the length of the bed
. The little wall mounted fans that come with boats are silly, they make a lot of noise
and do not really blow. I can't imagine leaving one of those on all the time and listening to it buzz. There are much better fans: these 12 volt box fans
quietly move much more air.
But... even with that we rarely closed the door to the aft berth in hot weather
. And it was still the hottest and stuffiest part of the boat.
The best solution I have seen for ventilating an 'aft berth under cockpit' was on a Van De Stadt. The cockpit bench had a section that was ~10" lower than the rest, and had a hatch on top of the lower section. The teak
strips were at the same level of the rest of the bench seat, so people could still sit there, but one could open this big hatch up underneath the seat and get plenty of airflow through it. That would be 'the ultimate', but involves a big fiberglass project
to retrofit. I also feel that a small hatch underneath the dodger
, in the standing part of the berth, adds a lot of good ventilation that works in most weather
(which the V-berth tends to not have).