Chinese scientists will start to drill a deep ice core at Kunlun station near Dome A in the near future. Recent work has predicted that Dome A is a location where ice older than 1 million years can be found. We model flow, temperature and the age of the ice by applying a three-dimensional, thermo-mechanically coupled full-Stokes model to a 70 km × 70 km domain around Kunlun station, using isotropic non-linear rheology and different prescribed anisotropic ice fabrics that vary the evolution from isotropic to single maximum at 1/3 or 2/3 depths. The variation in fabric is about as important as the uncertainties in geothermal heat flux in determining the vertical advection which in consequence controls both the basal temperature and the age profile. We find strongly variable basal ages across the domain since the ice varies greatly in thickness and any basal melting effectively removes very old ice in the deepest parts of the subglacial valleys. Comparison with dated radar isochrones in the upper one third of the ice sheet cannot sufficiently constrain the age of the deeper ice, with uncertainties as large as 500 000 yr in the basal age. We also assess basal age and thermal state sensitivities to geothermal heat flux and surface conditions. Despite expectations of modest changes in surface height over a glacial cycle at Dome A, even small variations in the evolution of surface conditions cause large variation in basal conditions which is consistent with basal accretion features seen in radar surveys.