Future climate change depends on properties of the climate system and the external forcing factors that drive the global energy budget. Among those properties are climate sensitivity, the rate at which heat is mixed into the deep ocean, and the aerosol forcing on the planet. In this dissertation, we use the newly updated Massachusetts Institute of Technology Earth System Model (MESM) to derive the joint probability distribution function (PDF) for model parameters that represent the aforementioned climate system properties. Climate sensitivity (ECS) in the model is set through an adjustment to the cloud feedback parameter. The vertical diffusion coefficient, Kv, represents the mixing of heat into the deep ocean by all mixing processes. The net anthropogenic aerosol forcing parameter, Faer, estimates the contribution of aerosol cooling to the global energy budget. Using an 1800-member ensemble of MESM runs where the model parameters have been systematically varied, we derive PDFs for the model parameters by comparing the model output against historical observations of surface temperature and global mean ocean heat content. In particular, we answer four main research questions: (1) How are the parameter PDFs derived using the MESM ensemble different from those using a previous version of the model?, (2) How do the estimates change when recent surface temperature and ocean heat content observations are included in the model diagnostics used to evaluate model performance?, (3) How does internal climate variability lead to uncertainty in the parameter estimates?, and (4) What impact do the changes in PDFs have on estimates of future warming, namely estimates of transient climate response (TCR)? We show that estimates of climate sensitivity increase and the aerosol forcing is less negative when using MESM. These shifts are the result of a new forcing suite used to drive the model. By extending the length of the model diagnostics one decade at a time, we show that recent temperature patterns impact our estimates of the climate system properties. The continued rise in surface temperature leads to higher values of ECS, while the increased rate of heat storage in the ocean leads to lower estimates of ECS and higher estimates of Kv. We show that the parameter distributions are sensitive to the internal variability in the climate system and that using a single variability estimate can lead to PDFs that are too narrow. Throughout the dissertation, we show that estimates of transient climate response are correlated with ECS and Kv. Namely, higher ECS and weaker Kv lead to higher values of TCR. When considering all of these factors, we arrive at our best estimate for the climate system properties. We estimate the 90-percent confidence interval for climate sensitivity to be 2.7 to 5.4 degrees C with a mode of 3.5 degrees C. Our estimate for Kv is 1.9 to 23.0 cm²s⁻¹ with a mode of 4.41 cm²s⁻¹. Faer is estimated to be between -0.4 and -0.04 Wm⁻² with a mode of –0.25 Wm⁻². Lastly, we estimate TCR to be between 1.4 and 2.1 degrees C with a mode of 1.8 degrees C.