Several practical applications of evolutionary computation possess objective functions that receive the design variables and externally given parameters. Such problems are termed contextual optimization problems. These problems require finding the optimal solutions corresponding to the given context vectors. Existing contextual optimization methods train a policy model to predict the optimal solution from context vectors. However, the performance of such models is limited by their representation ability. By contrast, warm starting methods have been used to initialize evolutionary algorithms on a given problem using the optimization results on similar problems. Because warm starting methods do not consider the context vectors, their performances can be improved on contextual optimization problems. Herein, we propose a covariance matrix adaptation evolution strategy with contextual warm starting (CMA-ES-CWS) to efficiently optimize the contextual optimization problem with a given context vector. The CMA-ES-CWS utilizes the optimization results of past context vectors to train the multivariate Gaussian process regression. Subsequently, the CMA-ES-CWS performs warm starting for a given context vector by initializing the search distribution using posterior distribution of the Gaussian process regression. The results of the numerical simulation suggest that CMA-ES-CWS outperforms the existing contextual optimization and warm starting methods.