If you know the exact state of a system, then it has zero entropy regardless of what that particular state happens to be. In this case, you also don't need thermodynamics to model the system's evolution, because you can predict its future exactly.

When you only know summary, average statistics of a system (such as its temperature), its entropy is nonzero, because your information about the system isn't enough to isolate a particular microstate. Instead you just have a distribution of many possibile microstates, any of which would match the measurements you know. The more possible system microstates there are that would agree with your data, the higher its entropy.