Do aeroshells really get hotter than the surface of the sun?

Question

This answer to How to design heatshield bluntness? says:

Curiosity reentry dumped about 98% of its entry energy into the atmosphere, the aeroshell can still get to be temps greater than the surface of the sun.

Of course the surface of the Sun is a bit ambiguous and the temperature of the photosphere varies by 1000 K every 70 kilometers, the technical definition of the surface is usually the point at which the visible light opacity reaches 2/3, (see What is the density profile within the Sun's photosphere? Which one of these is wrong?) but since we're talking about "white hot" things we can use something like the best fit to the Sun's spectrum or it's effective color temperature of almost 5,800 K.

That's pretty close to the temperature near the Sun's photosphere as it should be.

Question: Are there really parts of the aeroshell that get this hot? Or is that the temperature of the gas or plasma nearby?

For example, ASTM's 2015 news item New material has higher melting point than any known substance says:

Computations show that a material made with just the right amounts of hafnium, nitrogen, and carbon would have a melting point of more than 4400 K (7460°F). That's about two-thirds the temperature at the surface of the sun and 200 K higher than the highest melting point ever recorded experimentally.

See also https://matmatch.com/learn/material/metals-high-melting-point

Answer 1

This article says 1,930°C (2,200K) for Curiosity, which seem in line with peak Orion and Apollo values from this answer, 2,200°C (2,470K) and 5,000°F (3,000K).

As such, the surface material does not reach solar temperatures.

However, the gas and plasma immediately next to it can easily reach 10x solar temperature, and what is "surface" of the Sun other gas and plasma :)

Question: Are there really parts of the aeroshell that get this hot? Or is that the temperature of the gas or plasma nearby?

The later then, it is.