The temperature of a Fe-Cr-Ni alloy (304 stainless steel) has been measured during shock compression using a high-speed radiometric technique. Experiments were performed on high-quality thick films deposited on sapphire and LiF windows. The samples had no observable porosity or defects and closely meet the ideal criteria for shock temperature measurements. Data obtained with both Al2O3 and LiF windows are internally consistent, indicating that they remain transparent to high pressures and are thus suitable windows for shock temperature measurements. Our data yield stainless steel melting temperatures ranging from 4750¿310 K at 138 GPa to 5710¿340 K at 215 GPa, and additionally provide bounds on the initial Hugoniot temperatures of the sample between 5600¿340 K at 234 GPa (near the solidus) and 6580¿440 K at 283 (in the liquid field). Taken together, these data define a smooth curve for melting of the alloy up to 271 GPa and 5860 K, which should represent a point on the liquidus. Melting along the Hugoniot begins at approximately 234 GPa and 5600 K, as compared with 242 GPa and 6400 K for pure Fe. At the pressure of the inner core boundary, the melting point of 304 stainless steel is lower than that pure Fe by ≈1450 K, as compared with only 110 K at 1 atm. These results demonstrate that upon alloying with Ni and Cr the melting point depression of Fe and thus material likely to comprise the inner core increases with increasing pressure. ¿American Geophysical Union 1990