  We calculate the heating and cooling of the accreting white dwarf (WD) in the
ultracompact AM Canum Venaticorum (AM CVn) binaries and show that the WD can
contribute significantly to their optical and ultraviolet emission. We estimate
the WD's effective temperature, Teff, using the optical continuum for a number
of observed binaries, and show that it agrees well with our theoretical
calculations. Driven by gravitational radiation losses, the time averaged
accretion rate, <Mdot>, decreases monotonically with increasing Porb, covering
six orders of magnitude. If the short period (Porb<10 min) systems accrete at a
rate consistent with gravitational radiation via direct impact, we predict
their unpulsed optical/UV light to be that of the Teff>50,000$ K accreting WD.
At longer Porb we calculate the Teff and absolute visual magnitude, M_V, that
the accreting WD will have during low accretion states, and find that the WD
naturally crosses the pulsational instability strip. Discovery and study of
pulsations could allow for the measurement of the accumulated helium mass on
the accreting WD, as well as its rotation rate. Accretion heats the WD core,
but for Porb>40 minutes, the WD's Teff is set by its cooling as <Mdot>
plummets. For the two long period AM CVn binaries with measured parallaxes, GP
Com and CE 315, we show that the optical broadband colors and intensity are
that expected from a pure helium atmosphere WD. This confirms that the WD
brightness sets the minimum light in wide AM CVn binaries, allowing for
meaningful constraints on their population density from deep optical searches,
both in the field and in Globular Clusters.
