Probably not. Just off the top of my head I can't think of any situations where there was enough at stake for either of the superpowers to contemplate that.
South Africa did of course have a nuclear program, and even assembled some weapons (they remain the only country to voluntarily give up a nuclear capability once achieving it). It might just barely be possible to get them to go nuclear over something, but I'm not sure that would be enough to draw a US/USSR nuclear response unless it was directed at one of those powers in some way - perhaps a Soviet expeditionary unit committed to the region, although that itself is extremely difficult to plausibly arrange. Even so, the best you might get would be a tit-for-tat response which peters out pretty quickly. Put bluntly the superpowers didn't think Africa was important enough to devote that much effort to, IMO. Certainly not important enough to blow up the world over.