  SnSe monolayers experience a temperature induced two-dimensional Pnm2$_1 \to$
P4/nmm structural transformation precipitated by the softening of vibrational
modes. The standard theoretical treatment of thermoelectricity---which relies
on a zero temperature phonon dispersion and on a zero temperature electronic
structure---is incapable of describing thermoelectric phenomena induced by
structural transformations. Relying on structural data obtained from {\em ab
initio} molecular dynamics calculations that is utilized in a non-standard way
to inform of electronic and vibrational transport coefficients, the present
work establishes a general route to understand thermoelectricity across phase
transitions. Similar to recent experimental observations pointing to an
overestimated thermoelectric figure of merit $ZT$ past the transition
temperature, our work indicates a smaller $ZT$ when compared to its value
predicted by the standard paradigm. Its decrease is related to the dramatic
changes in the electrical conductivity and lattice thermal conductivity as the
structural transformation ensues. Though exemplified on a SnSe monolayer, the
method does not have any built-in assumptions concerning dimensionality, and
thus applicable to arbitrary thermoelectric materials in one, two, and three
dimensions.
