This paper extends the work of Pindyck by taking into consideration a large class family of different utility functions of economic agents. As in Pindyck, instead of consideringa social utility function that is characterized by constant relative risk aversion (C.R.R.A), we use the expo-power utility function of Saha. In fact, depending on the choice of the expo-power utility function parameters, we cover a diverse range1of utility functions and besides covering the other utility functions that a C.R.R.A omits, Expo-power function permits usto discern if under the other behaviors of economic agents, the willingness to pay remainsmore affected by uncertain outcomes than certain outcomes, when we vary the expectationand standard deviation of the temperature distribution probability. Our paper has maintained the small-tailed gamma distributions of temperature and economic impact of Pindyck, notonly because they hinder infinite future welfare losses (for an exponential utility function), but because it is easy to change some moments of the distribution (jointly or holding the othersfixed) while studying how uncertainty influences the willingness to pay as explained in Pindyck.