We prepare heralded single photons from a photon pair source based on non-degenerate four-wave mixing in a cold atomic ensemble via a cascade decay scheme. Their statistics shows strong antibunching with g(2)(0) < 0.03, indicating a near single photon character. In an optical homodyne experiment, we directly measure the temporal envelope of these photons and find, depending on the heralding scheme, an exponentially decaying or rising profile. The rising envelope will be useful for efficient interaction between single photons and microscopic systems like single atoms and molecules. At the same time, their observation illustrates the breakdown of a realistic interpretation of the heralding process in terms of defining an initial condition of a physical system.