  Double white dwarf (WD) binaries are increasingly being discovered at short
orbital periods where strong tidal effects and significant tidal heating
signatures may occur. We assume the tidal potential of the companion excites
outgoing gravity waves within the WD primary, the dissipation of which leads to
an increase in the WD's surface temperature. We compute the excitation and
dissipation of the waves in cooling WD models in evolving MESA binary
simulations. Tidal heating is self-consistently computed and added to the
models at every time step. As a binary inspirals to orbital periods less than
$\sim$20 minutes, the WD's behavior changes from cooling to heating, with
temperature enhancements that can exceed 10,000 K compared with non-tidally
heated models. We compare a grid of tidally heated WD models to observed
short-period systems with hot WD primaries. While tidal heating affects their
$T_{\rm eff}$, it is likely not the dominant luminosity. Instead these WDs are
probably intrinsically young and hot, implying the binaries formed at short
orbital periods. The binaries are consistent with undergoing common envelope
evolution with a somewhat low efficiency $\alpha_{\rm CE}$. We delineate the
parameter space where the traveling wave assumption is most valid, noting that
it breaks down for WDs that cool sufficiently, where standing waves may instead
be formed.
