  We consider large N U(N)^M thermal N=2 quiver gauge theories on S^1 x S^3. We
obtain a phase diagram of the theory with R-symmetry chemical potentials,
separating a low-temperature/high-chemical potential region from a
high-temperature/low-chemical potential region. In close analogy with the N=4
SYM case, the free energy is of order O(1) in the low-temperature region and of
order O(N^2 M) in the high-temperature phase. We conclude that the N=2 theory
undergoes a first order Hagedorn phase transition at the curve in the phase
diagram separating these two regions. We observe that in the region of zero
temperature and critical chemical potential the Hilbert space of gauge
invariant operators truncates to smaller subsectors. We compute a l-loop
effective potential with non-zero VEV's for the scalar fields in a sector where
the VEV's are homogeneous and mutually commuting. At low temperatures the
eigenvalues of these VEV's are distributed uniformly over an S^5/Z_M which we
interpret as the emergence of the S^5/Z_M factor of the holographically dual
geometry AdS_5 x S^5/Z_M. Above the Hagedorn transition the eigenvalue
distribution of the Polyakov loop opens a gap, resulting in the collapse of the
joint eigenvalue distribution from S^5/Z_M x S^1 into S^6/Z_M.
