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 that 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 ∼20 minutes, the WD's behavior changes from cooling to heating, with temperature enhancements that can exceed 10,000 K compared with nontidally 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 Teff, it is likely not the dominant luminosity. Instead, these WDs are probably intrinsically young and hot, implying that the binaries formed at short orbital periods. The binaries are consistent with undergoing common envelope evolution with a somewhat low efficiency αCE. 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.