  The chiral phase transition of the quark sector of QCD is investigated within
the Hamiltonian approach in Coulomb gauge. Finite temperatures $T$ are
introduced by compactifying one spatial dimension, which makes all
thermodynamical quantities accessible from the ground state on the spatial
manifold $\mathbb{R}^2 \times S^1(1/T)$. In the limit of a vanishing
quark-gluon coupling, 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 $107 \, \mathrm{MeV}$.
