The generation and transmission of planar, thermoacoustic (TAG) waves by the heating of a quiescent, isothermal, semi-infinite, gaseous medium’s boundary is investigated theoretically. For step and gradual changes in the boundary temperature of a Pr = 3/4 gas, long- and short-time asymptotes are derived for the pressure, velocity and temperature fields and for the wall heat flux. Then the method of Laplace transform with numerical inversion is used to solve the linearized equations for general wall heating conditions. By comparing the Laplace transform predictions with the asymptotic results and with experimental data, the numerical scheme is verified and found to be highly accurate. Finally, the nonlinear equations are solved numerically to assess their effect on wave characteristics and to determine the conditions under which the linear approximation is adequate.