The existing literature on climate change offers little guidance on why one specification or another of a "damages function" has been selected. Ideally, one wants a functional form that captures reality adequately, yet is analytically sufficiently tractable to yield useful results. This paper gives two plausible risk aversion axioms that a reduced form utility function of temperature change and the capacity to produce consumption might reasonably be required to satisfy. These axioms indicate that the standard-practice multiplicative specification of disutility damages from global warming, as well as its additive analogue, are special cases of this paper's theoretically derived utility function. Empirically, the paper gives some numerical examples demonstrating the surprisingly strong implications for economic policy of the distinction between additive and multiplicative disutility damages.