This paper discusses the dynamics of a novel energy harvester that converts heat into mechanical vibrations of two polyvinylidene fluoride (PVDF) piezoelectric cantilevers that generate electrical energy using a shape memory alloy (SMA) filament. The vibrations are generated by a symmetrical system of two masses placed on the SMA filament, which moves transversely due to its own longitudinal temperature contractions and extensions. Temperature differences over a heat source of constant temperature are the cause of the periodic changes in length of the SMA filament. An experimental setup was created to study the harvester by measuring the mass displacements and electrical voltages generated by the piezoelectric cantilevers. Data were obtained on the dependence of the output voltage and power on the load resistance of the consumer. The experimental results are validated by a multiphysics dynamical model, taking into account the relationships between the mechanical, thermal and electrical domains. The vibrational modeling of the SMA filament takes into account the hysteresis properties and their characteristics when the time gradient changes, leading to the appearance of minor and sub-minor hysteresis. Research has shown that from a heater with a constant temperature of 70 °C, the maximum power obtained is 3.6 μW at a load resistance of 4 MΩ, and a maximum voltage of 5.8 V was generated at a load resistance of 13 MΩ. An important feature of the proposed design is the possibility of miniaturizing the mechanical system.