Climate change has been classed as the greatest and urgent global issue facing humanity today, yet the empirics of the debate remain largely muted, more so with reference to sub-Saharan Africa (SSA), where the impact of warming global temperatures are forecasted to have the worst impact. This paper is a contribution to the empirics of climate change and its effect on sustainable economic growth in SSA using nonparametric regression techniques. We establish the following: the relationship between real GDP per capita on one hand and climate change on the other hand, is intrinsically linear and monotonically decreasing at a constant proportionate rate. This relationship holds for both temperature and precipitation.