I am from the South... and have lived in that area...
Go to weather.com and pull up Knoxville, TN...
Check out current temps... and look for the place to click for monthly and daily averages.
Dollywood is actually not in the mountains... There are some 'foothills' but that is it. The temperatures at Dollywood will be just has hot as the surrounding Knoxville area.. There will be no cooling due to altitude.
And, in July it can be HOT.. In the 90's.
It can be humid, so that does make it feel hot.
If June is possible I would recommend that you travel as early as is convenient.. The summer heat sets in towards the end of June.
If you want to do water rides or visit Splash Country, you will be glad that it is hot enough to swim... My pick would be mid to late June.
Right now it is early May, and it is still nice and cool... even tad chilly at night.
Outdoor pools generally open Memorial Day, but their water can still be chilly for a week or two.
There will be a major weather change in the next 8 weeks between the first week of May and the first week of July. So timing could possibly make a difference.
Have you been to the area before?
Do you know where you want to stay?
I know that there are a lot of DISers who have been and like to offer info and advice!