Logs of user queries from a search engine (such as Bing or Google) together with the links clicked provide valuable implicit feedback to improve statistical spoken language understanding (SLU) models. However, the form of natural language utterances occurring in spoken interactions with a computer differs stylistically from that of keyword search queries. In this paper, we propose a machine translation approach to learn a mapping from natural language utterances to search queries. We train statistical translation models, using task and domain independent semantically equivalent natural language and keyword search query pairs mined from the search query click logs. We then extend our previous work on enriching the existing classification feature sets for input utterance domain detection with features computed using the click distribution over a set of clicked URLs from search engine query click logs of user utterances with automatically translated queries. This approach results in significant improvements for domain detection, especially when detecting the domains of user utterances that are formulated as natural language queries and effectively complements to the earlier work using syntactic transformations.