Determining the temperature distribution of coronal plasmas can provide stringent constraints on coronal heating. Current observations with the Extreme ultraviolet Imaging Spectrograph onboard Hinode and the Atmospheric Imaging Assembly onboard the Solar Dynamics Observatory provide diagnostics of the emission measure distribution (EMD) of the coronal plasma. Here we test the reliability of temperature diagnostics using 3D radiative MHD simulations. We produce synthetic observables from the models, and apply the Monte Carlo Markov chain EMD diagnostic. By comparing the derived EMDs with the true distributions from the model we assess the limitations of the diagnostics, as a function of the plasma parameters and of the signal-to-noise of the data. We find that EMDs derived from EIS synthetic data reproduce some general characteristics of the true distributions, but usually show differences from the true EMDs that are much larger than the estimated uncertainties suggest, especially when structures with significantly different density overlap along the line-of-sight. When using AIA synthetic data the derived EMDs reproduce the true EMDs much less accurately, especially for broad EMDs. The differences between the two instruments are due to the: (1) smaller number of constraints provided by AIA data, (2) broad temperature response function of the AIA channels which provide looser constraints to the temperature distribution. Our results suggest that EMDs derived from current observatories may often show significant discrepancies from the true EMDs, rendering their interpretation fraught with uncertainty. These inherent limitations to the method should be carefully considered when using these distributions to constrain coronal heating.
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