An adaptive distributed estimation strategy is developed based on incremental gradient techniques. The proposed scheme addresses the problem of distributed linear estimation in a cooperative fashion, resulting in a distributed algorithm that can respond in real time to changes in the environment. Each node is allowed to communicate only with its immediate neighbor in order to exploit the spatial dimension while at the same time reducing the communications burden. A spatial-temporal energy conservation argument is used to evaluate the steady-state mean-square-error performance of the individual nodes across the adaptive distributed network. Computer simulations illustrate the results