  Two-dimensional topological insulators, and in particular quantum Hall
states, are characterized by an insulating bulk and a conducting edge.
Fractional states may host both downstream (dictated by the magnetic field) and
upstream propagating edge modes, which leads to complex transport behavior.
Here, we combine two measurement techniques, local noise thermometry and
thermal conductance, to study thermal properties of states with
counter-propagating edge modes. We find that, while charge equilibration
between counter-propagating edge modes is very fast, the equilibration of heat
is extremely inefficient, leading to an almost ballistic heat transport over
macroscopic distances. Moreover, we observe an emergent quantization of the
heat conductance associated with a strong interaction fixed point of the edge
modes. This new understanding of the thermal equilibration on edges with
counter-propagating modes is a natural route towards extracting the topological
order of the exotic 5/2 state.
