The average download time of a file is an important performance metric for a user in a peer-to-peer network. We point out that the common approach of analyzing the average download time based On average service capacity is fundamentally flawed,and show that spatial heterogeneity and temporal correlation in the service capacity over different paths are the two major factors that have negative impact on the average file download time. We then propose a simple and distributed algorithm that can completely remove this negative impact of the two factors and yield the smallest possible average download time for each user in the network.