Read the documentation, and specifically the description of the 'configuration' query, which explains how to get images.

http://docs.themoviedb.apiary.io/#get-%2F3%2Fconfiguration

Assorted API queries give you filenames. Choose your preferred resolution from those listed as available in the configuration data, add that and the filename to the base URL also given by the configuration data, and you've made yourself a link to a thumbnail.

If you're asking if the thumbnails themselves are ever base64 encoded directly into the JSON response, no.