The demand for materials and devices that are capable of controlling heat fl ux has attracted many interests due to desire to attain new sources of energy and on-chip cooling. Excellent properties of DNA make it as an interesting nanomaterial in future technologies. In this paper, we aim to investigate the thermal fl ow through two sequence combinations of DNA, e.g, (AT) 4 (CG) 4 (AT) 4 (CG) 4 and (CG) 8 (AT) 8 . Two interesting phenomena have been observed respectively. In the fi rst confi guration, an oscillatory thermal fl ux is observed. In this way, an oscillating heat fl ux from a stationary spatial thermal gradient is provided by varying the gate temperature. In the second confi guration, the system behaves as a constant heat current source. The physical mechanism behind each phenomenon is identifi ed. In the fi rst case, it was shown that the transition between thermal positive conductance and negative diff erential conductance implies oscillatory heat current. In the latter, the discordance between the phonon bands of the two coupled sequences results in constant thermal fl ow despite of increasing in temperature gradient.