Abstract Motivated by the requirements for the effective heat exchange with marine applications, the hydrothermal performances of the rectangular channel enhanced by the array of twisted-tape pin-fins in rolling and pitching motions were studied using the steady-state infrared thermography method. The distributions of endwall Nusselt number, the Fanning friction coefficients, and the thermal performance factors were measured at Reynolds numbers of 1500, 2500, 3500, 4500 and 5500 with the test channel in single pitching, single rolling and combined pitching-rolling motions. For each mode of swinging condition with the frequency of 0, 0.5, 0.667 or 0.833 Hz at each Reynolds number tested, four heater powers were applied to the test channel for exploring the buoyancy effect on the heat transfer performance. While the present pitching or rolling forces agitated the vortical flows developed in the pin–fin channel to augment strain rates for heat transfer enhancements, the synergetic heat transfer impact at the combined pitching-rolling mode suppressed the effectiveness of heat transfer enhancement attributed to the single pitching and single rolling motions. Relative to the static-channel conditions, the time-mean averaged Nusselt numbers in the single pitching, the single rolling and the combined pitching-rolling motions were modified to 0.88–1.31, 1.02–1.55 and 0.98–1.77 times of the static-channel Nusselt numbers with the corresponding elevations of friction factor to 1.05–2.59, 0.76–2.50 and 2.09–6.79 times of the static-channel references. At all the swinging conditions tested, the time-mean local and area-averaged Nusselt numbers were increased by enhancing the buoyancy level. The considerable pressured drop augmentations at the combined pitching and rolling modes led to the degradation of the hydrothermal performance from that with the single pitching or the single rolling motions. In addition to the newly devised array of twisted tapes as a passive heat transfer enhancement method, the individual and synergetic impacts of pitching and rolling motions on the detailed heat transfer distribution revealed by the present study went beyond the previous efforts in the literature. For assisting the relevant engineering applications, two set of empirical correlations that calculated the time-mean endwall averaged Nusselt number and Fanning friction coefficient of the present twisted-tape pin–fin channel in single pitching, single rolling and combined pitching-rolling motions were devised.