Talbot-Lau grating interferometer (TLGI) has great advantages in X-ray imaging contrasts, especially for low-Z materials, over conventional absorption contrast. A microstructured array anode target (MAAT) source offers significantly higher imaging throughput than the combination of an extended X-ray source paired with an absorption grating (also known as source grating). The performance of the MAAT source can be optimized with respect to the areal density, dimensions, and choice of material for the microstructured metal inserts (MMI) and the substrate in which they are embedded. In this paper, we analyze the X-ray generation efficiency per incident electron, relative fraction of X-rays generated by MMI and substrate, X-ray spectrum, and angular distribution via Monte Carlo simulation. Based on the simulation results, the optimal parameters are obtained for a MAAT with incident electron energies from 30 keV to 120 keV. The corresponding temperature distribution within the MAAT is also simulated for the optimal set of the parameters via finite element analysis. As demonstrated by the thermal analysis data, the maximum allowable electron-beam power loading was derived that allows a stable operation of the transmission MAAT.