Scaling down the dimensions of thermoacoustic sound sources (thermophones) improves efficiency by means of reducing speaker heat capacity. Recent experiments with nanoscale thermophones have revealed properties which are not fully understood theoretically. We develop a Green's function formalism which quantitatively explains some observed discrepancies, e.g., the effect of a heat-absorbing substrate in the proximity of the sound source. We also find a generic ultimate limit for thermophone efficiency. We verify the theory with experiments and finite difference method simulations which deal with thermoacoustically operated suspended arrays of nanowires. The efficiency of our devices is measured to be 1 order of magnitude below the ultimate bound. At low frequencies this mainly results from the presence of a substrate. At high frequencies, on the other hand, the efficiency is limited by the heat capacity of the nanowires. Measured sound pressure level and efficiency are in good agreement with simulations. We discuss the feasibility of reaching the ultimate limit in practice.