I often get the question, “What is the best variety of red raspberry to grow here in Mississippi”? My answer is usually a long silence before sputtering out, “I don’t recommend them”. Why not? Well, for one reason they are not tolerant of our heat during the summer. Red raspberries (Rubus ideaus) are not native to North America. In fact they come from northern Europe originally. Now, I’ve never been to northern Europe, but I am willing to bet it isn’t quite like Mississippi in the summertime. These raspberries also have problems in areas with up-and-down temperatures during the winter. Since they are generally have very good cold hardiness, they deacclimate quickly and can be damaged by late winter and early spring frosts and freezes. Years ago some work was done at Mississippi State University to breed a heat tolerant raspberry. The outcome of that was a release named ‘Dormanred’. ‘Dormanred’ is not pure Rubus idaeus, in fact it is part Rubus parvifolius. As for how it does in the heat, the answer to that is that it does well. It has a trailing growth habit and can produce a good amount of fruit. The downside? The fruit is dark-colored, sometimes crumbly, and not very delicious. Dump enough sugar on them and you won’t mind, but eating them fresh isn’t the same experience as a true red raspberry.
When I was a graduate student at the University of Arkansas I studied the photosynthetic capacity of red raspberries as an indicator of heat tolerance. The results were not encouraging among available varieties at the time (it was 15 years ago, but the varieties are still available). Red raspberries really prefer moderate temperatures (15-20 C) to high temperatures (30+C). I also included a blackberry in the study and it performed much better. You can download my paper on this here: Stafne et al. 2001. HortScience 36:880-883 Another part of the study looked at raspberry growth at two different locations in Arkansas. That is available here: http://arkansasagnews.uark.edu/483.pdf (starts on page 44).
In another paper I looked at several different genotypes, including ‘Mandarin‘. If you click the link you can read about ‘Mandarin’. It is difficult (if not impossible) to find at nurseries, but I did hear recently that a nursery in North Carolina is now propagating it. Not sure if or when it will be available to the general public, but Dr. Gina Fernandez (NCSU) is trying to get it reintroduced. It is one of the more promising raspberries out there for southern production — but it does have its problems too. You can download my paper that included ‘Mandarin’ here: Stafne et al. 2000. HortScience 35:278-280
Mandarin raspberry. Courtesy Dr. Gina Fernandez
I wish I could in good conscious recommend a raspberry for Mississippi. Some growers may have luck in situations where afternoon shade can be provided on a small scale. If ‘Mandarin’ becomes available I would recommend it on a trial basis for backyard and very small scale commercial growers, but until then we are stuck with ‘Dormanred’.
Mississippi Fruit and Nut Blog 
Have you done any studies on boysenberries? Some of them might have inherited the heat tolerance from the Blackberry side of their cross.
No, no studies on boysenberries. Even though boysenberries do have blackberry in their lineage it is a different species than we generally grow in the South. Rubus ursinus is the species associated with boysenberry and I’m not sure of the heat tolerance of it. I know that it is not especially cold hardy. The southern blackberry species that make up our current varieties (Rubus allegheniensis and Rubus argutus, primarily) are native to the southern U.S.