Counter-rotating-wave terms(CRWTs)are traditionally viewed to be crucial in open small quantum systems with strong system-bath dissipation.Here by exemplifying in a nonequilibrium qubit-phonon hybrid model,we show that CRWTs can play the significant role in quantum heat transfer even with weak system-bath dissipation.By using extended coherent phonon states,we obtain the quantum master equation with heat exchange rates contributed by rotating-wave-terms(RWTs)and CRWTs,respectively.We find that including only RWTs,the steady state heat current and current fluctuations will be significantly suppressed at large temperature bias,whereas they are strongly enhanced by considering CRWTs in addition.Furthermore,for the phonon statistics,the average phonon number and two-phonon correlation are nearly insensitive to strong qubit-phonon hybridization with only RWTs,whereas they will be dramatically cooled down via the cooperative transitions based on CRWTs in addition.Therefore,CRWTs in quantum heat transfer system should be treated carefully.