This paper reports refinement studies on the temporal coupling scheme and time-stepping management of TRACE/S3K, a dynamically coupled code version of the thermal-hydraulics system code TRACE and the 3D core simulator Simulate-3K. The studies were carried out for two test cases, namely a PWR rod ejection accident and the Peach Bottom 2 Turbine Trip Test 2. The solution of the coupled calculation, especially the power peak, proves to be very sensitive to the time-step size with the currently employed conventional operator-splitting. Furthermore, a very small time-step size is necessary to achieve decent accuracy. This degrades the trade-off between accuracy and performance. A simple and computationally cheap implementation of time-projection of power has been shown to be able to improve the convergence of the coupled calculation. This scheme is able to achieve a prescribed accuracy with a larger time-step size.