Following the pulsation spectrum of a white dwarf through the heating and cooling involved in a dwarf nova outburst cycle provides a unique view of the changes to convective driving that take place on timescales of months versus millenia for non-accreting white dwarfs. In 2019 January the dwarf nova V386 Ser (one of a small number containing an accreting, pulsating white dwarf), underwent a large amplitude outburst. Hubble Space Telescope ultraviolet spectra were obtained 7 and 13 months after outburst along with optical ground-based photometry during this interval and high-speed photometry at 5.5 and 17 months after outburst. The resulting spectral and pulsational analysis shows a cooling of the white dwarf from 21,020 K to 18,750 K (with a gravity log(g) = 8.1) between the two UV observations, along with the presence of strong pulsations evident in both UV and optical at a much shorter period after outburst than at quiescence. The pulsation periods consistently lengthened during the year following outburst, in agreement with pulsation theory. However, it remains to be seen if the behavior at longer times past outburst will mimic the unusual non-monotonic cooling and long periods evident in the similar system GW Lib.