Based on a complete set of J = 0 and J = 1 spatial isovector correlation functions calculated with N-F = 2 domain wall fermions we identify an intermediate temperature regime of T similar to 220-500 MeV (1.2T(c)-2.8T(c)), where chiral symmetry is restored but the correlators are not yet compatible with a simple free quark behavior. More specifically, in the temperature range T similar to 220-500 MeV we identify a multiplet structure of spatial correlators that suggests emergent SU(2)(cs) and SU(4) symmetries, which are not symmetries of the free Dirac action. The symmetry breaking effects in this temperature range are less than 5%. Our results indicate that at these temperatures the chromomagnetic interaction is suppressed and the elementary degrees of freedom are chirally symmetric quarks bound into color-singlet objects by the chromoelectric component of the gluon field. At temperatures between 500 and 660 MeV the emergent SU(2)(cs) and SU(4) symmetries disappear and one observes a smooth transition to the regime above T similar to 1 GeV where only chiral symmetries survive, which are finally compatible with quasifree quarks.