We investigate the heat generation Q in a quantum dot(QD), coupled to a normal metal and a superconductor,without electric bias voltage. It is found that Q is quite sensitive to the lead temperatures T_(L,R) and the superconductor gap magnitude △. At T_(L,R)<<ω_0(ω_0 is the phonon frequency), the superconductor affects Q only at △ <ω_0, and the maximum magnitude of negative Q appears at some △ slightly smaller than ω_0. At elevated lead temperature,contribution to Q from the superconductor arises at △,ranging from less than to much larger than ω_0. However, the peak value of Q is several times smaller than that in the case of T_(L,R)<< ω_0.Interchanging lead temperatures T_L and T_R leads to quite different Q behaviors, while this makes no difference for a normal-metal-quantum-dot-normal-metal system, and the QD can be cooled much more efficiently when the superconductor is colder. We investigate the heat generation Q in a quantum dot (QD), coupled to a normal metal and a superconductor, without electric bias voltage. It is found that Q is quite sensitive to the lead temperatures T_ (L, R) and the superconductor gap At T_ (L, R) << ω_0 (ω_0 is the phonon frequency), the superconductor affects Q only at Δ <ω_0, and the maximum magnitude of negative Q appears at some Δ slightly smaller than ω_0. At elevated lead temperature, contribution to Q from the superconductor arises at △, ranging from less than to much larger than ω_0. However, the peak value of Q is several times smaller than that in the case of T_ (L, R) << ω_0. Interchanging lead temperatures T_L and T_R leads to quite different Q behaviors, while this makes no difference for a normal-metal-quantum-dot-normal-metal system, and the QD can be cooled much more when when the superconductor is colder.