Sponsored search auctions (SSAs) have attracted a lot of research attention in recent years and different equilibrium concepts have been studied in order to understand advertisers' bidding strategies. However, the assumption that advertisers are perfectly rational in these studies is unrealistic in the real world. In this work, we apply the quantal response equilibrium (QRE), which is powerful in modeling bounded rationality, to SSAs. Due to high computational complexity, existing methods for QRE computation have very poor scalability for SSAs. Through exploiting the structures of QRE for SSAs, this paper presents an efficient homotopy-based algorithm to compute the QRE for large-size SSAs, which features the following two novelties: 1) we represent the SSAs as an Action Graph Game (AGG) which can compute the expected utilities in polynomial time; 2) we further significantly reduce redundant calculations by leveraging the underlying relations between advertisers' utilities. We also develop an estimator to infer parameters of SSAs and fit the QRE model into a dataset from a commercial search engine. Our experimental results indicate that the algorithm can significantly improve the scalability of QRE computation for SSAs and the QRE model can describe the real-world bidding behaviors in a very accurate manner.