Temperatures are predicted to soar into the 100's in NC in the next few days. Raspberries and even their more heat tolerant cousins blackberries will be stressed. The most important thing you can do at this time is to make sure your plants are well watered. This will help reduce the stress to the plant and enable your berries to continue to ripen and get plump.
Raspberry roots are usually in the top 10" of soil, while blackberries roots can be much deeper. However, the majority of the water is taken up by the roots in the top 6" of soil. Water stress before or during harvest can seriously reduce productivity. Water is the most critical factor for optimal fruit growth and primocane development, a berry is afterall more than 90% water! A shortage of water will limit fruit size and also the number and diameter of primocanes for next years crop.