  The chiral phase transition of the quark sector of QCD is investigated within
the Hamiltonian approach in Coulomb gauge. Finite temperature T is introduced
by compactifying one spatial dimension, which makes all thermodynamical
quantities accessible from the ground state on the spatial manifold
$\small\mathbb{R}^2 \times S^1(1/T)$. Neglecting the coupling between quarks
and transversal gluons, the equations of motion of the quark sector are solved
numerically and the chiral quark condensate is evaluated and compared to the
results of the usual canonical approach to finite-temperature Hamiltonian QCD
based on the density operator of the grand canonical ensemble. For zero bare
quark masses, we find a second-order chiral phase transition with a critical
temperature of about 92 MeV. If the Coulomb string tension is adjusted to
reproduce the phenomenological value of the quark condensate, the critical
temperature increases to 118 MeV.
