  In frustrated quantum magnetism, chiral spin liquids are a particularly
intriguing subset of quantum spin liquids in which the fractionalized parton
degrees of freedom form a Chern insulator. Here we study an exactly solvable
spin-3/2 model which harbors not only chiral spin liquids but also spin liquids
with higher-order parton band topology -- a trivial band insulator, a Chern
insulator with gapless chiral edge modes, and a second-order topological
insulator with gapless corner modes. With a focus on the thermodynamic
precursors and thermal phase transitions associated with these distinct states,
we employ numerically exact quantum Monte Carlo simulations to reveal a number
of unconventional phenomena. This includes a heightened thermal stability of
the ground state phases, the emergence of a partial flux ordering of the
associated $\mathbb{Z}_2$ lattice gauge field, and the formation of a thermal
Majorana metal regime extending over a broad temperature range.
