Theoretical Modeling of the Thermal State of Accreting White Dwarfs Undergoing Classical Nova Cycles

White dwarfs (WDs) experience a thermal renaissance when they receive mass from a stellar companion in a binary. For accretion rates of less than 10^-8 M_☉ yr^-1, the freshly accumulated hydrogen/helium envelope ignites in a thermally unstable manner that results in a classical nova (CN) outburst and ejection of material. We have undertaken a theoretical study of the impact of the accumulating envelope on the thermal state of the underlying WD. This has allowed us to find the equilibrium WD core temperatures (T_c), the CN ignition masses (M_ign), and the thermal luminosities for WDs accreting at rates of 10^-11 to 10^-8 M_☉ yr^-1. These accretion rates are most appropriate for WDs in cataclysmic variables (CVs) of P_orb ≲ 7 hr, many of which accrete sporadically as dwarf novae. We have included ³He in the accreted material at levels appropriate for CVs and find that it significantly modifies the CN ignition mass. We compare our results with several others from the CN literature and find that the inclusion of ³He leads to lower values of M_ign for ⟨⟩ ≳ 10^-10 M_☉ yr^-1 and that for ⟨⟩ values below this the particular author's assumption concerning T_c, which we calculate consistently, is a determining factor. Initial comparisons of our CN ignition masses with measured ejected masses find reasonable agreement and point to ejection of material comparable to that accreted.