Anomalous heating phenomena observed in free-piston shock tunnel HIEST is numerically investigated in terms of radiation from upstream high-temperature gas. For assessing recently reported heating levels that depends on model size, we first estimate heat fluxes over two different size test models through axi-symmetric Navier-Stokes simulations with thermochemical nonequilibrium chemistry. For the small test model, the convective heat flux is significantly larger than the radiative heat flux, and the anomalous heating does not appear remarkably even with an assumption of the radiative heating from the upstream gas. On the other hand, the anomalous heating can be generated for the large test model with relatively large radiative heat flux compared to the convective one. If the anomalous heating is attributed to the radiation from the upstream gas, difference in contributions of the radiative heating between two models can explain the scaling effect. We also calculate flowfield in the acceleration sections of HIEST and directly evaluate the radiative heat flux from the upstream gas. The accelerated flow is stagnated at the diaphragms and releases the considerable radiation. In the low enthalpy condition, the computed radiative flux reaches a level of the experiments, while that for the high enthalpy case becomes higher than the measured one.