I have a bunch of degenerate particles in a heat bath, which I can "measure" some of their properties to approximate the temperature of the heat bath. Like energy at ground state, 2nd, etc, and their degeneracies. But I was told that the exact temperature of the heat bath cannot be measured and only the approximation can be made. I was reading my stats mechanics book and all I can find is something about thermal equilibrium requiring a Boltzmann distribution and a formulation to find Temperature of a heat bath of non-degenerate particles. I tried searching the internet for some more information but I keep ending up with research papers that have nothing to do with my question.