Energy-intensive infrastructure may tie up fossil energy use and carbon emissions for a long time after investment, and thus be crucial for the ability to control long-run emissions. Much or most of the resulting carbon emissions can often be eliminated later, through a retrofit that may however be costly. This paper studies the joint decision to invest in such infrastructure, and retrofit it later, given that future climate damages are uncertain and follow a geometric Brownian motion process with positive drift. We find that higher climate cost volatility (for given unconditional expected costs) then delays the retrofit decision by increasing the option value of waiting to invest. The initial infrastructure is also chosen with higher energy intensity, further increasing total emissions, when volatility is higher. We provide conditions under which higher climate cost volatility increases total expected discounted climate damage from the infrastructure, which happens in a wide set of circumstances.