We have carried out the first quasi-static evolutionary model sequence with time-variable accretion in which the combined heating effect of boundary layer irradiation (including stellar rotation) and compressional heating on the underlying white dwarf accretor has been included. In the present study, we focus mainly on the behavior of the surface observables of the accreting white dwarf. This initial exploration followed the thermal evolution of a 0.6 M white dwarf in a dwarf nova over many dwarf nova accretion cycles. Accretion rates of ≈10−8 M yr−1, for outburst duration of days to weeks, are followed by a shutoff of the radial infall during dwarf nova quiescence. The matter is assumed to accrete “softly” with the same entropy as the white dwarf outer layers, but a fraction of the energy liberated in the boundary layer is assumed to be absorbed by the outer layer of the star (boundary layer irradiation). Accretion is resumed and shut off repeatedly at intervals of months to simulate the thermal evolution of the white dwarf in typical dwarf novae. The timescale of the white dwarf cooling is such that after a complete (outburst + quiescence) cycle, the surface of the white dwarf has not yet completely cooled down: the star has not yet readjusted and does not reach thermal equilibrium. When the evolution of the white dwarf is followed for 125 cycles (about 8 yr), the effective temperature (Teff) of the underlying white dwarf increases as a function of time (t) as log(Teff) = a log(t), where a > 0. We find that a itself decreases with increasing temperature. The inclusion of the boundary layer irradiation has no detectable effect on this particular result over the timescale studied here. When the boundary layer irradiation is taken into account, the effective surface temperature of the accreting white dwarf can increase by more than ≈20,000 K (in addition to the increase due to compressional heating) during outburst. During quiescence the outermost layer of the star quickly radiates away the energy absorbed during outburst. The overall fraction of the outer layer of the star thermally affected by the compressional heating is of the order of the mass accreted, namely, ≈10−8 M during a complete run. These results indicate that after a long evolution time of many accretion cycles, the effective surface temperature of the white dwarf will increase substantially. We discuss the application of the sequence to HST studies of the observed heating of white dwarfs in dwarf novae. We also examine the effect of compressional heating on the outer envelope structure, which directly demonstrates that there is a significant heating effect. We suggest that the envelope thermal structure resulting from compression and irradiation should be a crucial component in understanding the envelope structure of a prenova white dwarf.