Earthdata Search Client supports natural language spatial and temporal searches by leveraging a few different libraries. Spatial searches are parsed by CLAVIN and referenced against Geonames. Temporal searches are parsed by the Stanford Temporal Tagger (SUTime).
Spatial searches within EDSC work best when search for cities, states, or city and state combinations. CLAVIN does make certain assumptions about the city you are looking for. If you search for "Paris", it will assume you mean Paris, France. If you are looking for a different Paris, you will need to further specify which Paris you are looking for. You may also perform searches for well-known regions such as "New England" or "United Kingdom".
Temporal searches can be performed both by typing in exact datetimes or by performing relative searches (such as "yesterday" or "last month").
And finally, EDSC has login in place to parse out the keywords to be used for searching against the CMR. An example search query using all of these features would look something like:
land surface temperature in Dallas last decade
Here's a link to the results for that query: results. Notice that spatial and temporal extents have been set and a "land surface temperature" query has been performed.