The widespread use of the IEEE 802.11 MAC as a layer-2 protocol for wireless local area networks has generated an extensive literature on its performance modeling. However, most of the available studies evaluate the capacity of WLANs in saturated conditions, while very little has been done on investigating the interactions between the 802.11 MAC protocol and the various transport protocols that are used to deliver users' traffic. Recently there have been renewed efforts to understand and model the TCP dynamics in 802.11 WLANs. In general, these models employ multi-dimensional discrete-time Markov chains to analyze the distributions of the number of TCP packets enqueued in the stations' buffers. Then, they exploit those distributions to derive both the average number of active TCP stations and the aggregate TCP throughput. However, this approach may rapidly lead to the explosion of the model state-space when the number of TCP flows is large. In this technical report we propose a novel modeling approach by developing an average-value analysis of TCP performance in 802.11 WLANs. Our model intuitively characterizes the equilibrium conditions for the network, and this method yields a precise estimate of the throughput of persistent TCP flows. Extensive simulations validate the accuracy of our analysis.