Recent numerical simulations of hypersonic double-cone experiments overpredict the heat-transfer rate to the model by about 20%. We present a systematic analysis of the experimental facility and the physical modeling to explain this discrepancy. Nozzle flowfield simulations are used to investigate the effect of vibrational nonequilibrium in the test section. These simulations show that the vibrational modes of the nitrogen gas freeze near the nozzle throat conditions, resulting in an elevated vibrational temperature in the test section. This lowers the kinetic energy flux, reducing the heat transfer to the model. The effect of slip boundary conditions is also studied, and it is shown that weak accommodation of vibrational energy at the surface further reduces the heat-transfer rate to the model. The combination of these two effects brings the predicted heat-transfer rate into agreement with the experiments. In addition, weak flow nonuniformity in the test section is shown to slightly modify the predicted separation zone, further improving the agreement.