penguinande,

to the DIS Camping Board

.
Well we have folks here who can, do, and have tent camp(ed) in June to August but they drive and come prepared with portable air conditioners, extra rain flies, and the like. And it helps if you are an experienced camper and not a newbie to it.
I would tent camp any month other than June-September because those months have heat, humidity, and rain showers (wash, rinse, repeat). If I had to sometime in that window it would be as early in June as I could make it.
Also in the fall and spring, the weekends in particular fill up with "locals" coming in for short camping trips and the tentable sites are usually in demand then. So get your reservation in as far in advance as you can. If you can't, people do piece together their dates by getting multiple reservations.
Finally since you are flying, you can choose to ground ship some camping gear ahead of you and send it home the same way to simplify what you take on the plane. Just label it "Hold for guest arrival on 08/01/15" or something like that.
So to answer your question in the title of your thread, ANYTIME is a good time to camp at the Fort.
Bama Ed