Gardenspots:
I have been growing Baba in Northern Virginia for pretty close to 15 years. I don't know about the guru part though.
Baba behaves exactly the same way as any other "everbearing" red raspberry. New canes grow up in spring (primocanes), and by late summer and into fall produce their major crop. If, at the end of the season, you choose not to cut the canes down to the ground and allow them to over-winter, they become "floricanes" the next season, and will set a small, earlier-season crop.
The canes that are bearing a small crop for you now -- the ones that you planted -- are floricanes that grew up last season. Once they have fruited, their cycle is complete, and they should be cut down right to the ground. The future of your berries lies in the new primocanes that are growing up and that will bear later in the season with a much heavier crop. Many people (myself included), choose to skip the early crop entirely since the crop is so small and the old canes tend to get in the way. So I cut all of the canes down to the ground over the winter and begin afresh every season. Whether you try to get an additional early crop from the floricanes is your option.
But do not prune the new canes that are growing up, since they bear most heavily on the ends, and they normally do not need it. If they become heavily laden with berries they may tend to fall over when 4-feet tall or so, but you can simply string a wire down the center of the patch and provide them with some support. It may be worth your while to do this if your primocanes are very vigorous.
The principal advantage of Baba, and the basis for its original patent (now expired) is its resistance to heat. But it is also a productive berry of excellent quality. You mention that heat is a problem in your part of the country, but don't mention where that part is. I assume California. This berry was originally found as a chance seedling near Los Angeles, and is well adapted to that climate. But is also does well in mine, which is quite different.
Don Yellman, Great Falls, VA
Q