Yes, disparate distribution problems and rich/poor nation disparity is a big issue -- Africa for example, as you point out, has both.
Hopefully, several candidate vaccines will make it to approval. Moderna's apparently requires less extreme cooling. Others, even less cooling. Having multiple vaccines, with different characteristics, is potentially one of the great success stories here.
Also, I saw somewhere that Pfizer-Biontech is working on a powder form, not needing the cooling.
Current Pfizer-Biontech vaccine cooling requirements: -70C (-94F) during shipment. Apparently less, once delivered, if administered within a few days of delivery. I can visualize the lines at the pharmacy whenever a "new batch" arrives! It will be like the old days of ticket sale line-ups for concerts everybody knew would sell-out. Or "box-store" line-ups in March. Wait in line for a couple hours and somebody will come out to announce, "Sorry folks, we're sold-out today". Ideally, there would be online appointments -- we'll see. Reminds of:
Chili Peppers: "Standing in line ..."