The technique of acoustic travel time tomography (ATOM) employs the travel-time of early reflections to calculate the distribution of air temperature through an entire room. The number of detected early reflections in the room impulse response (RIR) which stands for the desired sound paths inside the room, has a significant impact on the resolution of reconstructed temperatures. In this study, the possibility of utilizing an array of directional sound sources for ATOM measurements is investigated. To compensate for the number of sound paths not appearing due to the directivity of the sound source, the consideration of high-energy third order reflections is proposed. For this purpose, the image source model (ISM) algorithm is developed to simulate the early reflections up to third-order image sources. The results indicate that the sufficient number of sound paths can ensure a proper tomography reconstruction.