In continuum mechanics, the constitutive models are usually based on the Cauchy-Born (CB) hypothesis which seeks the intrinsic characteristics of the material via the atomistic information and it is valid in small deformation. The main purpose of this thesis is to investigate the temperature effect on the stability and size dependency of Cauchy-Born hypothesis and a novel temperature-dependent multi-scale method is developed to investigate the role of temperature on surface effects in the analysis of nano-scale materials. Three-dimensional temperature-related Cauchy-Born formulation are developed for crystalline structure and the stability and size dependency of temperature-related...