  We calculate the stellar evolution of both white dwarfs (WDs) in AM CVn
binaries with orbital periods of $P_{\mathrm{orb}} \approx 5-70$ minutes. We
focus on the cases where the donor starts as a $M_{\mathrm{He}} < 0.2 \,
M_{\odot}$ Helium WD and the accretor is a $M_{\mathrm{WD}} > 0.6 \, M_{\odot}$
WD. Using Modules for Experiments in Stellar Astrophysics (MESA), we
simultaneously evolve both WDs assuming conservative mass transfer and angular
momentum loss from gravitational radiation. This self-consistent evolution
yields the important feedback of the properties of the donor on the mass
transfer rate, $\dot{M}$, as well as the thermal evolution of the accreting WD.
Consistent with earlier work, we find that the high $\dot{M}$'s at early times
forces an adiabatic evolution of the donor for $P_{\mathrm{orb}} < 30$ minutes
so that its mass-radius relation depends primarily on its initial entropy. As
the donor reaches $ M_{\mathrm{He}} \approx 0.02-0.03 \, M_{\odot}$ at
$P_{\mathrm{orb}} \simeq 30 $ minutes, it becomes fully convective and could
lose entropy and expand much less than expected under further mass loss.
However, we show that the lack of reliable opacities for the donor's surface
inhibit a secure prediction for this possible cooling. Our calculations capture
the core heating that occurs during the first $\approx 10^7$ years of accretion
and continue the evolution into the phase of WD cooling that follows. When
compared to existing data for accreting WDs, as seen by Cheng and collaborators
for isolated WDs, we also find that the accreting WDs are not as cool as we
would expect given the amount of time they have had to cool.
