A recent study by Bahr et al. found that "healthy" gut microbes increased non-aerobic resting metabolism by 16%, compared to gut microbes being treated by risperidone. Risperidone is an antipsychotic drug that causes weight gain and Bahr et al. were trying to determine why. In addition to to the article, their university issued a non-technical press release on the article.
This article doesn't exactly answer your question but does provide a good staring place.