Millimeter wavelength radio telescopes require a high surface and pointing precision, which in steerable open-air telescopes is obtained by a stiff or homologous construction and elaborate thermal control. The perturbing thermal loads and wind loads can also be reduced by protecting the telescope by a radome or astrodome, as applied on several operating telescopes. However, for the new generation telescopes of 30-m to 50-m diameter the radome or astrodome is very large and costly, and it is a priori not certain to which extent the internal thermal climate must be controlled, for instance, by forced air-conditioned ventilation, to obtain a telescope of good radio performance. We present data from the Onsala and Haystack radomes to illustrate agreement between measurements and thermal model calculations, and we use similar calculations to investigate the thermal behavior of a very large astrodome and radome. The accuracy of the calculations is sufficient for design and operational purposes.