Linearising thermal radiation
A radiative resistance is always between two
bodies $(i,j)$ with a temperature difference. In general,
the flow of heat between $(i)$ and $(j)$ has the form:
$$
Q_{j\rightarrow i} = \sigma\cdot A_{i,j}\left(Tj^4-T_i^4\right)
$$
-
$\sigma = 5.73 \times 10^{-8} W/m^2/K^4$ (Stefan-Bolzmann constant)
-
$A_{i,j} = $ factor with dimension of area $[m^2]$,
dependent on emission coefficients, radiative areas and, last but not least:
view factors.
-
$T = $ temperature
There is a Wikipedia reference about all this.
The heat flow can be written as the admittance $\gamma_{i,j}$ of a resistor,
times the temperature difference:
$$
Q_{j\rightarrow i} = \gamma_{i,j}\left(Tj-T_i\right)
$$
Where the admittance - though linearized reasonably well - is still dependent
on the temperatures:
$$
\gamma_{i,j} = \sigma\cdot A_{i,j}\left(Tj^2+T_i^2\right)\left(Tj+T_i\right)
$$
So iterations may be necessary, but the hard part is in $A_{i,j}$ and the view factors, most of the time.