We present numerical results for the thermodynamic limit of the one-dimensional symmetric Kondo lattice over the full temperature range, obtained by using a recently developed Monte Carlo technique. In particular, we compare spin correlations with RKKY predictions and two-impurity results, and note the opening of a gap as the temperature is lowered. We discuss the relevance of our results to various theoretical treatments of Kondo and Anderson lattice models. © 1990 The American Physical Society.