We examine observational consequences of the hypothesis that there is no steady coronal heating, the solar corona instead being heated episodically, such that each short burst of heating is followed by a long period of radiative cooling. We calculate the form of the resulting contribution to the differential emission measure (DEM), and to a convenient related function that we term the "differential energy flux" (DEF). On analyzing observational data for the quiet solar atmosphere, we find that the "upper branch" of the DEM, corresponding to temperatures above 105 K, can be interpreted in terms of episodic energy injection at coronal temperatures. For episodic heating, the magnitude of the DEM depends on the rate of injection of electrons of coronal temperature into a vertical column of unit cross sectional area. The required value of this quantity is close to the rate at which spicules inject electrons into the corona. It is suggested that the complete DEM may be interpreted as the combined effect of many small-scale injections with an appropriate distribution of parameters.