  Recent theoretical studies inspired by experiments on the Kitaev magnet
$\alpha$-RuCl$_3$ highlight the nontrivial impact of phonons on the thermal
Hall conductivity of chiral topological phases. Here we introduce mixed
mesoscopic-macroscopic devices that allow refined thermal-transport probes of
non-Abelian spin liquids with Ising topological order. These devices feature a
quantum-coherent mesoscopic region with negligible phonon conductance, flanked
by macroscopic lobes that facilitate efficient thermalization between chiral
Majorana edge modes and bulk phonons. We show that our devices enable $(i)$
accurate determination of the quantized thermal Hall conductivity, $(ii)$
identification of non-Abelian Ising anyons via the temperature dependence of
the thermal conductance, and most interestingly $(iii)$ single-anyon detection
through heat-based anyon interferometry. Analogous results apply broadly to
phonon-coupled chiral topological orders.
