  We investigate thermal properties of the X-Cube model and its
$\mathbb{Z}_{p}$ `clock-type' ($p$X-Cube) extension. In the latter, the
elementary spin-1/2 operators of the X-Cube model are replaced by elements of
the Weyl algebra. We study different boundary condition realizations of these
models and analyze their finite temperature dynamics and thermodynamics. We
find that (i) no finite temperature phase transitions occur in these systems.
In tandem, employing bond-algebraic dualities, we show that for Glauber type
solvable baths, (ii) thermal fluctuations might not enable system size
dependent time autocorrelations at all positive temperatures (i.e., they are
thermally fragile). Qualitatively, our results demonstrate that similar to
Kitaev's Toric code model, the X-Cube model (and its $p$-state clock-type
descendants) may be mapped to simple classical Ising ($p$-state clock) chains
in which neither phase transitions nor anomalously slow glassy dynamics might
appear.
