A micromechanics approach was utilized to investigate the thermally induced stress fields developed in the fiber and matrix of continuous fiber reinforced polymer matrix composites at cold temperatures typical of spacecraft operating temperatures. Results from a finite element stress analysis of a periodic array of fibers were compared to the closed-form solution of the composite cylinder model for several fiber/matrix materials. The influence of microstructural geometry, constituent properties, and fiber volume fraction were investigated. The results of this investigation showed that the assumed microstructural geometry of the composite (i.e., composite cylinder, square or hexagonal array) did affect the distributions and magnitudes of thermally induced stresses. The matrix stresses were shown not to be strong functions of the fiber properties. Matrix stresses increased in absolute value with increasing fiber volume fraction, V(f). A global/local analysis was used to approximate the stresses in localized regions of high V(f), constrained by a lower global V(f).