The efficient heat transfer resulting from flow boiling in microchannel heat sinks can help dissipate high heat fluxes from high-density electronic devices across a small temperature difference. However, practical implementation challenges unique to two-phase flow boiling, as compared to single-phase liquid cooling, have prevented its widespread adoption. A primary challenge is the occurrence of dynamic two-phase flow instabilities, such as pressure drop oscillations (PDO), that have the potential to degrade heat transfer performance or trigger premature critical heat flux (CHF) under some conditions. Under other conditions, PDOs are observed to have little to no impact on performance. One factor proposed by modeling studies to be responsible for this discrepancy in observations of the effect of dynamic instabilities on performance is the thermal capacitance of the heat sink, though this has not been confirmed by experiments. In this study, the effect of thermal capacitance on the transient thermal response of a heat sink experiencing PDOs is examined through use of a dynamic two-phase flow model and experiments. Flow boiling experiments are performed with a controlled compressible volume upstream of parallel-microchannel heat sinks having either a large or a small thermal capacitance. In accordance with the behavior predicted by our model, when thermal capacitance is reduced, the pressure drop oscillation frequency is found to decrease and temperature swings in the heat sink become more severe. Additionally, the experimentally measured CHF limit is diminished in the heat sink at smaller thermal capacitance. These results reveal thermal capacitance as a critical parameter that determines how much dynamic instabilities degrade flow boiling performance in a microchannel heat sink.