Converting heavy oil into valuable chemical products is a novel application of non-thermal plasma. However, the interaction between plasma and liquid is a complex process, including shock wave, heat transfer, electrical discharge and chemical reactions. In this paper, we investigate the effects of plasma heating on the discharge stability. Heptane and 1-methylnaphthalene are used as model compounds of heavy oil, and treated within argon and hydrogen in a coaxial DBD reactor, respectively. The DBD is powered by a nanosecond pulsed power source for higher chemical reactivity. The reactor is rapidly heated by the plasma in both cases. As the reactor temperature is approaching the boiling point (370 K) of the heptane, some dark areas come into being and expand above the liquid. Especially when the heptane is boiling, the plasma is almost extinguished except a small area near the inlet. The plasma restores when the heptane is exhausting, and transits into a diffusive DBD when the heptane is depleted. In the case of the methylnaphthalene with a higher boiling point (523 K), the discharge is more stable and gradually reaches its thermal equilibrium (430 K) in 40 min. Dark areas occur after 40 min. The reason for the formation of these dark areas is discussed in terms of the saturated vapor pressure and gap voltage. It is the vapor that increases the breakdown voltage of the primary discharge, and finally results in the instability of the discharge.