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: $$ Q_{j\rightarrow i} = \sigma\cdot A_{i,j}\left(Tj^4-T_i^4\right) $$ 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.