Driving is a complex task that is known to cause highly individual stress responses. Here we study heart rate variability (HRV) during automobile driving compared with being at rest. We focus on time-dependent variations in the scaling properties of the RR intervals by applying a newly developed dynamical detrended fluctuation analysis (DDFA). In particular, we study whether DDFA brings additional insights to the HRV analysis carried out by conventional measures in the time and frequency domain. We utilize the publicly available PhysioNet database for 16 drivers, whose ECG was recorded during 35–60 min of driving on public roads, preceded and followed by 15 min rest periods. The extracted RR intervals are then analyzed through the conventional HRV measures, followed by DDFA analysis that yields the time- and scale-dependent scaling exponents $\alpha(t, s)$. The temporal fidelity of the method permits accurate determination of distributions of $\alpha(t, s)$ in relatively short segments of data. We find that even when the HRV measures show clear differences between driving and being at rest, the subjects exhibit highly individual cardiac responses to the experiment. at the individual level, however, DDFA gives detailed information on the dynamic changes in HRV which are often hidden in the conventional measures.