The nanoflare model of solar coronal heating is based on the idea that ubiquitous tiny, independent heating events occur on individual sub-resolution strands within coronal loops. Each heating event raises its strand plasma to temperatures (6–10 MK) that are greater than the average active region temperature (about 2 MK). After the impulsive energy release, the loop strand increases in density and cools by conduction and radiation. The strand spends more time at higher density in the radiative cooling phase than it does in any other phase of the heating and cooling cycle. Thus, even when observed on spatial scales larger than the unresolvable individual strands, the solar atmosphere is expected to exhibit an overall cooling trend. Evidence for this has been presented based on correlations among light curves from AIA’s six EUV channels. While this supports the nanoflare model of coronal heating, AIA’s lack of temperature fidelity means that precise cooling information for small locations or single events are less than conclusive. Here we report results from an investigation of time-lag diagnostics based on EUV light curves derived from stare spectra obtained with a new EIS study designed to investigate time lags in non-flaring active regions. This study observes line emission from ten successive ionization stages of iron (VIII–XVII, 0.45–4 MK), as well as Fe XXIII (seen in flares and microflares) and lines formed at lower temperatures. We find evidence of post-nanoflare cooling in AR 12759 from 2.8 to 0.45 MK, but note that not all locations cool to temperatures this low, possibly indicating a mixture of medium and low frequency nanoflares. The AR periphery is cooler than its core, and exhibits post-nanoflare cooling only from 1.7 to 1.4 MK, suggestive of higher frequency nanoflares.