In many heat transfer related applications, there is a need for a stable, constant supply temperature. As a result, the integration of intermittent renewable sources of heat into these processes can prove to be challenging, requiring special temperature smoothing devices or strategies. This study focuses on the application of phase change materials integrated into a double tube heat exchanger as a possible thermal smoothing device. The objective of this study is to evaluate the ability of the exchanger to smoothen out temperature variations within the cold stream outlet while the hot stream is subject to oscillating inlet conditions. A computational fluid dynamics approach is used where a numerical model is developed, validated and then used to model the conjugate heat transfer within the heat exchanger. Four organic phase change materials (PCM) with different phase change temperatures were selected for investigation (myristic, octadecane, eicosane, and wax) to study the relationship between melting temperature and stabilization performance. A parametric study was then conducted by varying the Reynolds number of the flow as well as temperature oscillation period and amplitude to study the sensitivity of the system. The results confirm the potential of a phase change material-based thermal capacitor at dampening oscillations across the heat exchanger.