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 TL,R and the superconductor gap magnitude △.At TL,R 《 w0 (w0 is the phonon frequency),the superconductor affects Q only at △ < w0,and the maximum magnitude of negative Q appears at some △ slightly smaller than w0.At elevated lead temperature,contribution to Q from the superconductor arises at △,ranging from less than to much larger than w0.However,the peak value of Q is several times smaller than that in the case of TL,R 《 w0.Interchanging lead temperatures TL and TR 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.