The generation and transmission of linear and nonlinear thermoacoustic (TAG) waves in a confined gaseous medium, with a Prandtl number of 3/4, are investigated theoretically. The linearized equations are solved using the Laplace transform method with numerical inversion to obtain the pressure and temperature distributions in the cavity and the wall heat flux for various wall heating conditions. The nonlinear equations are solved accurately with finite differences. The differences between the linear and nonlinear waves are delineated. During the expansion phase, the nonlinear wave temperature dips below the average medium temperature. This cooling phenomenon is not exhibited by linear waves. The theoretical predictions are critically compared with Brown and Churchill’s experimental observations from 1995.