My understanding is that it shouldn’t even be glowing. The pressure of the earth above is acting as a counter against the excitement of the molecules within the alloy as it tries to become a liquid. At the center, the pressure is believed to be so great that it would prevent that excitement, and without that excitement there would be no glow.
When steel (or other metals) begin to glow, they are beginning to melt and are in a pliable state. The inner core shouldn’t even be pliable. I can’t find the exact melting point of nickel and iron at 330+ GPa, but I remember it being significantly higher than the 5000° C – 6000° C expected.
All of this is highly theoretical. The existence of a solid inner core and liquid outer core are measured indirectly during earthquakes, and the temperatures and pressures are computed based on models. There is no way for us to directly measure it.