Sensitive observations of the quiet Sun observed by EIT on the SOHO satellite in high-temperature iron-line emission originating in the corona are presented. The thermal radiation of the quiet corona is found to fluctutate significantly, even on the shortest time scale of 2 min and in the faintest pixels. The power spectrum of the emission measure time variations is approximately a power law with an exponent of 1.79 ± 0.08 for the brightest pixels and 1.69 ± 0.08 for the average and the faintest pixels. The more prominent enhancements are identified with previously reported X-ray network flares (Krucker et al., 1997) above the magnetic network of the quiet chromosphere. In coronal EUV iron lines they are amenable to detailed analysis suggesting that the brightenings are caused by additional plasma injected from below and heated to slightly higher temperature than the preexisting corona. Statistical investigations are consistent with the hypothesis that the weaker emission measure enhancements originate from the same parent population. The power input derived from the impulsive brightenings is linearly proportional to the radiative loss in the observed part of the corona. The absolute amount of impulsive input is model-dependent. It cannot be excluded that it can satisfy the total requirement for heating. These observations give strong evidence that a significant fraction of the heating in quiet coronal regions is impulsive.