  We discuss the instanton-dyon liquid model with $N_f$ Majorana quark flavors
in the adjoint representation of color $SU_c(2)$ at finite temperature. We
briefly recall the index theorem on $S^1\times R^3$ for twisted adjoint
fermions in a BPS dyon background of arbitrary holonomy, and use the ADHM
construction to explicit the adjoint anti-periodic zero modes. We use these
results to derive the partition function of an interacting instanton-dyon
ensemble with $N_f$ light and anti-periodic adjoint quarks. We develop the
model in details by mapping the theory on a 3-dimensional quantum effective
theory with adjoint quarks with manifest $SU(N_f)\times Z_{4N_f}$ symmetry.
Using a mean-field analysis at weak coupling and strong screening, we show that
center symmetry requires the spontaneous breaking of chiral symmetry, which is
shown to only take place for $N_f=1$. For a sufficiently dense liquid, we find
that the ground state is center symmetric and breaks spontaneously flavor
symmetry through $SU(N_f)\times Z_{4N_f}\rightarrow O(N_f)$. As the liquid
dilutes with increasing temperature, center symmetry and chiral symmetry are
restored. We present numerical and analytical estimates for the transition
temperatures.
