The Advanced Regional Prediction System is utilized to examine the evolution of the nocturnal boundary layer observed within Arizona's Meteor Crater, a small enclosed basin, on quiescent nights during the 2006 Meteor Crater Experiment field campaign. Two aspects of the observed basin atmosphere are investigated: a quasi steady-state three-layer temperature structure, including an isothermal layer away from the basin floor, and the intrusion of a regional-scale cold air drainage flow into the basin. In general, the two-dimensional numerical simulations are able to reproduce the salient features of the nocturnal boundary layer inside Meteor Crater. A combination of increasingly cold air intruding into the basin and pooling near the basin floor and compensating adiabatic ascent yield an isothermal layer over a large depth of the basin atmosphere. A series of experiments are then conducted in order to examine the sensitivity of basin thermal structure to upstream terrain slope, basin width, and the presence of a rim surrounding the basin. In the case of a large basin of O(10 km) in diameter, the cold air intrusion process remains, but the larger basin volume yields greater dilution of the cold air intruding into the basin, and a weak inversion develops inside the basin away from the floor. In the case of a small basin with the same dimensions as Meteor Crater but with flat upstream terrain, the influence of the surrounding terrain on basin cooling is negligible. Last, the presence of a rim surrounding the basin is found to not be necessary for isothermal layer development.