We just got finished with a Caribbean cruise (my first cruise) through a different cruise line. We had a balcony room and while it was nice, I get terrible eczema when exposed to the sun/heat for long periods of time. The A.C. in our room almost seemed non-existent and from what I have read, it depends on if the surrounding rooms leave their balcony doors open or not.
I have heard that some people bring small fans with them or get the cabin steward to assist (something we didn't think to ask