  Materials exhibiting topological order host exotic phenomena that could form
the basis for novel developments in areas ranging from low-power electronics to
quantum computers. The past decade has witnessed multiple experimental
realizations and thousands of predictions of topological materials. However, it
has been determined that increasing temperature destroys topological order,
restricting many topological materials to very low temperatures and thus
hampering practical applications. Here, we propose a material realization of
temperature promoted topological order. We show that a semiconducting oxide
that has been widely used in lead-acid batteries, $\beta$-PbO$_2$, hosts a
topological semimetallic phase driven by both thermal expansion and
electron-phonon coupling upon increasing temperature. We identify the interplay
between the quasi-two-dimensional nature of the charge distribution of the
valence band with the three-dimensional nature of the charge distribution of
the conduction band as the microscopic mechanism driving this unconventional
temperature dependence. Thus, we propose a general principle to search for and
design novel topological materials whose topological order is stabilized by
increasing temperature. This provides a clear roadmap for taking topological
materials from the laboratory to technological devices.
