In this paper, a quaternary dielectric soft-contact rotary triboelectric nanogenerator (QDSR-TENG) of low frictional resistance is fabricated for combining TENG with a shape memory alloy (SMA) engine. The introduction of rabbit fur brush and FEP brush results in charge pumps with a partially soft contact structure. Benefiting from the low friction loss of the structure, the QDSR-TENG can operate stably and continually for 100k cycles without significant output degradation. The SMA engine exhibits thermally induced phase transformation and super-elasticity and can be utilized for harnessing waste heat energy. The thermal-driven QDSR-TENG can operate with a water source of 43 degrees C with a distinguishable response to the variation of temperatures. Such a low starting temperature not only promotes the harvesting of low-grade thermal energy, but also results in a self-monitoring industrial cooling water system. The coupled elastocaloric power and cooling cycle proposed in the thermal-driven QDSR-TENG opens a new paradigm for the application in energy harvesting and smart sensing.