  We investigate the nonequilibrium quantum heat transfer in a triangle-coupled
spin-boson system within a three-terminal setup. By including the
nonequilibrium noninteracting blip approximation approach combined with the
full counting statistics, we analytically obtain the steady state populations
and heat currents. The negative differential thermal conductance and giant heat
amplification factor are clearly observed at strong qubit-bath coupling. %and
the heat amplification is dramatically suppressed in the moderate coupling
regime. Moreover, the strong interaction between the gating qubit and gating
thermal bath is unraveled to be compulsory to exhibit these far-from
equilibrium features.
