Little (like few) has negative polarity. It implies "only a little" or "not very much", or sometimes "contrary to what you might have expected, only a little".
A little (and a few) do not have this implication - they are neutrally stating that the number or amount is small, and saying nothing about what you might have expected.
In your example, someone asks for coffee, and the speaker responds that there is not much left—so the person asking cannot have any. In this case they would use
Sorry, there is little coffee left in the thermos.
...although this is a strange response: unless it is further explained or already known that what little there is has been set aside for a third person, there is no reason not to give the requester the last of the coffee.
If the speaker was able to provide more coffee, they would say
Yes, there is a little coffee left in the thermos.
meaning "there is still some left, and you may have it."