Recently, there has been a strong interest in the climate emergency and the human health impacts of climate change. Although estimates have been quoted, the modeling methods used have either been simplistic or opaque, making it difficult for policy makers to have confidence in these estimates. Providing central estimates of health impacts, without any quantification of their uncertainty, is deficient because such an approach does not acknowledge the inherent uncertainty in extreme environmental exposures associated with spiraling climate change and related health impacts. Furthermore, presenting only the uncertainty bounds around central estimates, without information on how the uncertainty in each of the model parameters and assumptions contribute to the total uncertainty, is insufficient because this approach hides those parameters and assumptions which contribute most to the total uncertainty. We propose a framework for calculating the catastrophic human health impacts of spiraling climate change and the associated uncertainties. Our framework comprises three building blocks: (A) a climate model to simulate the environmental exposure extremes of spiraling climate change; (B) a health impact model which estimates the health burdens of the extremes of environmental exposures; and (C) an analytical mathematical method which characterizes the uncertainty in (A) and (B), propagates the uncertainty in-between and through these models, and attributes the proportion of uncertainty in the health outcomes to model assumptions and parameter values. Once applied, our framework can be of significant value to policy makers because it handles uncertainty transparently while taking into account the complex interactions between climate and human health.