Simple climate models can be used to estimate the global temperature response to increasing greenhouse gases. Changes in the energy balance of the global climate system are represented by equations that necessitate the use of uncertain parameters. The values of these parameters can be estimated from historical observations, model testing, and tuning to more complex models. Efforts have been made at estimating the possible ranges for these parameters. This study continues this process, but demonstrates two new constraints. Previous studies have shown that land-ocean temperature differences are only weakly correlated with global mean temperature for natural internal climate variations. Hence, these temperature differences provide additional information that can be used to help constrain model parameters. In addition, an ocean heat content ratio can also provide a further constraint. A pulse response technique was used to identify relative parameter sensitivity which confirmed the importance of climate sensitivity and ocean vertical diffusivity, but the land-ocean warming ratio and the land-ocean heat exchange coefficient were also found to be important. Experiments demonstrate the utility of the land-ocean temperature difference and ocean heat content ratio for setting parameter values. This work is based on investigations with MAGICC (Model for the Assessment of Greenhouse-gas Induced Climate Change) as the simple climate model.