[en] Solar EUV images recorded by the EUV Imaging Telescope (EIT) on SOHO have been used to evaluate temperature and density as a function of position in two largescale features in the corona observed in the temperature range of 1.0-2.0MK. Such observations permit estimates of longitudinal temperature gradients (if present) in the corona and, consequently, estimates of thermal conduction and radiative losses as a function of position in the features. We examine two relatively cool features as recorded in EIT's Feix/x (171Å) and Fexii (195Å) bands in a decaying active region. The first is a long-lived loop-like feature with one leg, ending in the active region, much more prominent than one or more distant footpoints assumed to be rooted in regions of weakly enhanced field. The other is a near-radial feature, observed at the West limb, which may be either the base of a very high loop or the base of a helmet streamer. We evaluate energy requirements to support a steady-state energy balance in these features and find in both instances that downward thermal conductive losses (at heights above the transition region) are inadequate to support local radiative losses, which are the predominant loss mechanism. The requirement that a coronal energy deposition rate proportional to the square of the ambient electron density (or pressure) is present in these cool coronal features provides an additional constraint on coronal heating mechanisms.