We explore the effects of changing heating parameters in closed coronal loops on the intensity of Atmospheric Imaging Assembly (AIA) observations. Using EBTEL (Enthalpy-Based Thermal Evolution of Loops) hydrodynamic simulations, we produce realizations of coronal loops with a series of heating events randomly drawn from a power law distribution. We repeat this procedure for multiple loop lengths, heating intensities, and characteristic heating frequencies to investigate how each of these parameters individually and in combination influences observable loop properties. We generate AIA intensities from the corona and transition region for each realization. The variations within and between models generated with these different parameters illustrate the sensitivity of narrowband imaging to the details of coronal heating. Using insights from this analysis, we generate images of observed coronal active regions using the GX Simulator SSW IDL package and interpret the causes of discrepancies between the models and observations.