Quasi-constant heating at the footpoints of loops leads to evaporation and condensation cycles of the plasma: thermal non-equilibrium (TNE). This phenomenon is believed to play a role in the formation of prominences and coronal rain. However, it is often discarded to be involved in the heating of warm loops as the models do not reproduce observations. Recent simulations have shown that these inconsistencies with observations may be due to oversimplifications of the geometries of the models. In addition, our recent observations reveal that long-period intensity pulsations (several hours) are common in solar coronal loops. These periods are consistent with those expected from TNE. The aim of this paper is to derive characteristic physical properties of the plasma for some of these events to test the potential role of TNE in loop heating. We analyzed three events in detail using the six EUV coronal channels of SDO/AIA. We performed both a Differential Emission Measure (DEM) and a time-lag analysis, including a new method to isolate the relevant signal from the foreground and background emission. For the three events, the DEM undergoes long-period pulsations, which is a signature of periodic heating even though the loops are captured in their cooling phase, as is the bulk of the active regions. We link long-period intensity pulsations to new signatures of loop heating with strong evidence for evaporation and condensation cycles. We thus witness simultaneously widespread cooling and TNE. Finally, we discuss the implications of our new observations for both static and impulsive heating models.

Using Fourier and wavelet analysis, we critically re-assess the significance of our detection of periodic pulsations in coronal loops. We show that the proper identification of the frequency dependence and statistical properties of the different components of the power spectra provies a strong argument against the common practice of data detrending, which tends to produce spurious detections around the cut-off frequency of the filter. In addition, the white and red noise models built into the widely used wavelet code of Torrence & Compo cannot, in most cases, adequately represent the power spectra of coronal time series, thus also possibly causing false positives. Both effects suggest that several reports of periodic phenomena should be re-examined. The Torrence & Compo code nonetheless effectively computes rigorous confidence levels if provided with pertinent models of mean power spectra, and we describe the appropriate manner in which to call its core routines. We recall the meaning of the default confidence levels output from the code, and we propose new Monte-Carlo-derived levels that take into account the total number of degrees of freedom in the wavelet spectra. These improvements allow us to confirm that the power peaks that we detected have a very low probability of being caused by noise.