Clusters of galaxies have been extensively used to determine cosmological parameters. A major difficulty in making the best use of Sunyaev-Zel'dovich (SZ) and X-ray observations of clusters for cosmology is that using X-ray observations it is difficult to measure the temperature distribution and therefore determine the density distribution in individual clusters of galaxies out to the virial radius. Observations with the new generation of SZ instruments are a promising alternative approach. We use clusters of galaxies drawn from high-resolution adaptive mesh refinement cosmological simulations to study how well we should be able to constrain the large-scale distribution of the intracluster gas (ICG) in individual massive relaxed clusters using AMiBA in its configuration with 13 1.2 m diameter dishes (AMiBA13) along with X-ray observations. We show that non-isothermal β models provide a good description of the ICG in our simulated relaxed clusters. We use simulated X-ray observations to estimate the quality of constraints on the distribution of gas density, and simulated SZ visibilities (AMiBA13 observations) for constraints on the large-scale temperature distribution of the ICG. We find that AMiBA13 visibilities should constrain the scale radius of the temperature distribution to about 50% accuracy. We conclude that the upgraded AMiBA, AMiBA 13, should be a powerful instrument to constrain the large-scale distribution of the ICG.