Space‐based infrared telescopes will be of great importance in the search for extrasolar planets, and in their subsequent investigation. Such telescopes benefit enormously from radiative cooling. We have investigated this cooling with the aid of a Monte‐Carlo model of a cylindrical telescope tube shielded from the Sun by two flat plates. Our primary concern has been to establish to what extent radiative exchanges have to be modeled more accurately than has been the case up to now. We have shown that the equilibrium temperatures depend significantly on the directionality of the radiative properties of the materials coating the tube and shields. Also significant is the polarization of the radiation exchanged between the tube and shields, the change of radiative properties with wavelength and temperature, and the spacing between the shields and tube. There is a need for further measurements of infrared radiative properties at cryogenic temperatures, and we are planning to make some.