Momma J,
If I were tent camping, I would primarily be concerned about conditions at night when sleeping. For first week of June, on average, the lows are 68-70F. And the low comes in the hour before sunrise so, again on average, it would be a few degrees warmer at 10pm or so when you turn in (or later for some). So that's kinda right on the line for me. And who knows if temps will be "average" when it's your turn to be there?
You might get by with a fan to circulate air in the tent rather than go to the expense of getting an AC that you might not use very often.
Can you wait till a week or two before you go to watch the forecast and make a decision then?
Bama Ed