Does the Fermi-Dirac distribution for massless fermions have any special interest? Historically, the blackbody radiation (basically a system of photons in thermal equilibrium) played a pivotal role in the discovery of quantum theory. 
Initially, people used to think of neutrinos to be massless particles. But unlike photons, they are fermions and extremely weakly interacting. As an academic curiosity or classroom discussion, does any textbook discuss the distribution of massless fermions in equilibrium and its features?
 A: Assuming that I understood your question, in condensed matter physics there are sometimes massless fermions. For example electrons in graphene, near the so-called $K$-point, are effectively massless and are described by a Dirac Hamiltonian, with linear dispersion. The Fermi-Dirac distribution that describe them is then of massless fermions. It is used extensively.
A: Neutrinos can be in equilibrium extreme dense matter like inside of core collapse supernova core called proto-neutron star. The density reaches $10^{12}$-$10^{13}$ gr/cm$^{3}$ depending on progenitor mass. So the created neutrinos from $ e^{-} + e^{+} \rightarrow \nu_{\alpha} + \overline{\nu}_{\alpha} $ , $ e^{\pm} + X \rightarrow e^{\pm} + X +  \nu_{\alpha} + \overline{\nu}_{\alpha}$ reactions etc. trapped into the core and be in equilibrium. Typically, neutrinos have MeV temperatures when they are emitted from neutrinosphere (the layer where they can freely stream).
Also, in principle, neutrinos have to be in equilibrium in the early stage of big bang like photons. Like cosmic microwave background radiation, there should be relic neutrinos streamed from neutrino horizon.
For more information, see Giunt's book pg 525 and chapter 16.
