Consider the integrated circuit (IC) generating power $P$ inside a box of surface area $A$. The energy balance equation is below.
$$ P = \sigma A \left(\epsilon_{IC}T_{IC}^4 - \epsilon_{B}T_{B}^4 \right) + h_i A \left(T_{IC} - T_B\right) $$
The first term is the net radiation flow with the Stefan-Boltzmann constant, emissivities and temperatures. The second is the convection flow inside the box with the convection coefficient. Assuming that you know all materials related values, this is one equation with two unknown temperatures.
The energy balance equation from the box to the air is written as below.
$$ \sigma A \left(\epsilon_{IC}T_{IC}^4 - \epsilon_{B}T_{B}^4\right) + h_i A \left(T_{IC} - T_B\right) = \sigma A \left(\epsilon_{B}T_{B}^4 - \epsilon_{a}T_{a}^4 \right) + h_a A \left(T_{B} - T_a\right)$$
The energy going in to the box from the inside equals the energy leaving the box from the outside. Assuming you know all the materials related values and the air temperature $T_a$, this is a second equation with the same two unknowns.
In principle, the problem is solvable. In practice, the easiest first approach is to neglect all radiation terms. This step gives these two equations.
$$ P = h_i A \left(T_{IC} - T_B\right) = h_a A \left(T_{B} - T_a\right)$$
This shows you that the temperature at the IC relative to the box will be balanced to first order by the ratio of internal to external convection coefficients.
$$ \frac{\left(T_{IC} - T_B\right)}{\left(T_{B} - T_a\right)} = \frac{h_i}{h_a}$$
Since the inside of the box is stagnate while the outside can be moving air, $h_i < h_a$ in general. Therefore, $\left(T_{IC} - T_B\right) > \left(T_{B} - T_a\right)$ in general. The IC will be hotter relative to the box than the box is relative to the air around it.
This first order approximation can be used as seed guesses to the full-blown equation with radiation. I might recommend a graphical solution in the full blown case.
