Excellent coordinated observations of NOAA active region 12712 were obtained during the flight of the High-resolution Coronal Imager (Hi-C) sounding rocket on 2018 May 29. This region displayed a typical active region core structure with relatively short, high-temperature loops crossing the polarity inversion line and bright "moss"located at the footpoints of these loops. The differential emission measure (DEM) in the active region core is very sharply peaked at about 4 MK. Further, there is little evidence for impulsive heating events in the moss, even at the high spatial resolution and cadence of Hi-C. This suggests that active region core heating is occurring at a high frequency and keeping the loops close to equilibrium. To create a time-dependent simulation of the active region core, we combine nonlinear force-free extrapolations of the measured magnetic field with a heating rate that is dependent on the field strength and loop length and has a Poisson waiting time distribution. We use the approximate solutions to the hydrodynamic loop equations to simulate the full ensemble of active region core loops for a range of heating parameters. In all cases, we find that high-frequency heating provides the best match to the observed DEM. For selected field lines, we solve the full hydrodynamic loop equations, including radiative transfer in the chromosphere, to simulate transition region and chromospheric emission. We find that for heating scenarios consistent with the DEM, classical signatures of energy release, such as transition region brightenings and chromospheric evaporation, are weak, suggesting that they would be difficult to detect.