This work presents an experimental study of a nanosecond repetitively pulsed dielectric barrier discharge interacting with a transient laminar flame propagating in a channel of height near the quenching distance of the flame. The discharge and the flame are of comparable size, and the discharge is favoured at a location where it is coupled with the reaction zone and burnt gas. The primary goal is to determine how the discharge evolves on the time scale of the flame passage, with the evolution driven by the changing gas state produced by the moving flame front. This work complements the large body of work investigating the effect of plasma to modify flame dynamics, by considering the other side of the interaction (how the discharge is modified by the flame). The hot gas produced by the combustion had a strong effect on the discharge, with the discharge preferentially forming in the region of hot combustion products. The per-pulse energy deposited by the discharge was measured and found to increase with the size of the discharge region and applied voltage. The pulse repetition frequency did not have a direct impact on the per-pulse energy, but did have an effect on the morphology and size of the discharge region. Two distinct discharge regimes were observed: uniform and filamentary (microdischarges). Higher pulse repetition frequencies and faster-cooling combustion products were more likely to transition to the filamentary regime, while lower frequencies and slower-cooling combustion products maintained a uniform regime for the entirety of the time the discharge was active. This regime transition was influenced by the ratio of the time scale of fluid motion to the pulse repetition rate (with no noticeable impact caused by the reduced electric field), with the filamentary regime preferentially observed in situations where this ratio was small. This work demonstrates the importance of considering how the discharge properties will change due to combustion processes in applications utilizing plasma assistance for transient combustion systems.