Structures in space environments, whether operating in orbit or on the extraplanetary surfaces are exposed to a wide range of temperature variations. The severity of the temperature effect has been demonstrated and underlined by the failure of several space structures in fulfilling their intended missions in the past. It has been realized that the extreme temperature gradient possible in a structure subjected to space environment gives a host of structural problems that are not normally found in the terrestrial structures. These include thermal buckling, deformation, stresses, vibration and oscillatory motion, nutational body motion, and material degradation. This paper begins with the survey of relevant published literature within the last four decades on temperature effects in space structures. It discusses salient features of the thermal effects, the problems that were identified, and the remedies adopted. Furthermore, the paper attempts to identify new potential basic problems that may arise in space structures due to extreme temperature variations and their possible solution in light of the technological advancement of the modern era. Emphasis is given to the potential thermally induced vibration effects in large and lightweight structures in orbit and on the moon. Coupled thermal-mechanical structural vibration is examined. Work in progress to develop a refined analysis of an orbital truss structure with thermal effects is outlined.