For an interactive agent, such as task-oriented spoken dialog systems or chatbots, measuring and adapting to Customer Satisfaction (CSAT) is critical in order to understand user perception of an agent's behavior and increase user engagement and retention. However, an agent often relies on explicit customer feedback for measuring CSAT. Such explicit feedback may result in potential distraction to users and it can be challenging to capture continuously changing user's satisfaction. To address this challenge, we present a new approach to automatically estimate CSAT using acoustic and lexical information in the Alexa Prize Socialbot data. We first explore the relationship between CSAT and sentiment scores at both the utterance and conversation level. We then investigate static and temporal modeling methods that use estimated sentiment scores as a mid-level representation. The results show that the sentiment scores, particularly valence and satisfaction, are correlated with CSAT. We also demonstrate that our proposed temporal modeling approach for estimating CSAT achieves competitive performance, relative to static baselines as well as human performance. This work provides insights into open domain social conversations between real users and socialbots, and the use of both acoustic and lexical information for understanding the relationship between CSAT and sentiment scores.