This paper is concerned with some optimal control problems for the
Stefan-Boltzmann radiative transfer equation.
The objective of the optimisation is to obtain a desired temperature profile
on part of the domain by controlling the source or the shape of the domain.
We present two problems with the same objective functional:
an optimal control problem
for the intensity and the position of the heat sources and
an optimal shape design problem where
the top surface is sought as control. The problems are analysed and
first order necessity conditions in form of variation inequalities are