The AIA 304 Å channel on board the Solar Dynamics Observatory (SDO) offers a unique view of $\approx 10^{5}\text{ K}$
≈
10
5
K
plasma emitting in the He ii 304 Å line. However, when observing off-limb, the emission of the (small) cool structures in the solar atmosphere (such as spicules, coronal rain and prominence material) can be of the same order as the surrounding hot coronal emission from other spectral lines included in the 304 Å passband, particularly over active regions. In this paper, we investigate three methods based on temperature and morphology that are able to distinguish the cool and hot emission within the 304 Å passband. The methods are based on the Differential Emission Measure (DEM), a linear decomposition of the AIA response functions (RFit) and the Blind Source Separation (BSS) technique. All three methods are found to produce satisfactory results in both quiescent and flaring conditions, largely removing the diffuse corona and leading to images with cool material off-limb in sharp contrast with the background. We compare our results with co-aligned data from the Interface Region Imaging Spectrograph (IRIS) in the SJI 1400 Å and 2796 Å channels, and find the RFit method to best match the quantity and evolution of the cool material detected with IRIS. Some differences can appear due to plasma emitting in the $\log T=5.1\,\text{--}\,5.5$
log
T
=
5.1
–
5.5
temperature range, particularly during the catastrophic cooling stage prior to rain appearance during flares. These methods are, in principle, applicable to any passband from any instrument suffering from similar cool and hot emission ambiguity, as long as there is good coverage of the high-temperature range.