Climate change is expected to have many impacts on the environment, including changes in ozone concentrations at the surface level. A key public health concern is the potential increase in ozone-related summertime mortality if surface ozone concentrations rise in response to climate change. Although ozone formation depends partly on summertime weather, which exhibits considerable inter-annual variability, previous health impact studies have not incorporated the variability of ozone into their prediction models. A major source of uncertainty in the health impacts is the variability of the modeled ozone concentrations. We propose a Bayesian model and Monte Carlo estimation method for quantifying health effects of future ozone. An advantage of this approach is that we include the uncertainty in both the health effect association and the modeled ozone concentrations. Using our proposed approach, we quantify the expected change in ozone-related summertime mortality in the contiguous United States between 2000 and 2050 under a changing climate. The mortality estimates show regional patterns in the expected degree of impact. We also illustrate the results when using a common technique in previous work that averages ozone to reduce the size of the data, and contrast these findings with our own. Our analysis yields more realistic inferences, providing clearer interpretation for decision making regarding the impacts of climate change.