An adaptive distributed strategy is developed based on incremental techniques. The proposed scheme addresses the problem of linear estimation in a cooperative fashion, in which nodes equipped with local computing abilities derive local estimates and share them with their predefined neighbors. The resulting algorithm is distributed, cooperative, and able to respond in real time to changes in the environment. Each node is allowed to communicate with its immediate neighbor in order to exploit the spatial dimension while limiting the communications burden at the same time. A spatial-temporal energy conservation argument is used to evaluate the steady-state performance of the individual nodes across the entire network. Computer simulations illustrate the results.