  We investigate the effect of quantum phase slips on a helical quantum wire
coupled to a superconductor by proximity. The effective low-energy description
of the wire is that of a Majorana chain minimally coupled to a dynamical
$\mathbb{Z}_2$ gauge field. Hence the wire emulates a matter-coupled gauge
theory, with fermion parity playing the role of the gauged global symmetry.
Quantum phase slips lift the ground state degeneracy associated with unpaired
Majorana edge modes at the ends of the chain, a change that can be understood
as a transition between the confined and the Higgs-mechanism regimes of the
gauge theory. We identify the quantization of thermal conductance at the
transition as a robust experimental feature separating the two regimes. We
explain this result by establishing a relation between thermal conductance and
the Fredenhagen-Marcu string order-parameter for confinement in gauge theories.
Our work indicates that thermal transport could serve as a measure of non-local
order parameters for emergent or simulated topological quantum order.
