The transient aerothermodynamic processes in a gas-cooled reactor are described in a simplified manner to illustrate some of the fundamental physical phenomena involved, to provide some approximate but useful methods of analysis, and to aid in the understanding and use of more complex computer solutions. The transient heat balance equation for an element of a single reactor channel is derived in terms of aerothermodynamic time constants, and typical analytic solutions for transients are presented. This equation is used in generating the time-dependent equation for the channel exhaust gas temperature. The single-channel analysis is extended to multiple channels. A method for determining the approximate transient temperature envelopes for various reactor components is presented. The effects of aerodynamic and thermal coupling between different reactor channels are illustrated. Some of the simplifying assumptions are investigated with respect to the conditions under which they are valid.