  We investigate the local thermal transport in a quantum trimer of harmonic
oscillators connected to two thermal baths. The coupling between them are
augmented by complex phases which leads to the quantum control of the local
atypical heat current between two oscillators connected to the same heat bath.
Our study reveals that this atypical heat current is a consequence of the
lifting of the dark mode and the modulation of this current is due to variation
in system bath correlations. The proposed quantum system may find application
in quantum thermal and memory devices by leveraging the heat current.
