Climate change will increase the risk of temperature extremes. Induced innovation could offset some of this threat. This paper explores the demand and supply for climate adaptation innovation in a market economy. Climate change induces this innovation because the rising temperatures increase demand for self protection products and for profit firms respond to these incentives. We then augment the model to introduce climate skeptics. Such skeptics reject the claim that the world is warming and thus do not increasingly demand adaptation products. We study how the economy's rate of adaptation innovation, cross city migration, real estate pricing and the welfare of agents with rational expectations are all affected by the presence of such skeptics.