Harvesting small thermal gradients effectively to generate electricity still remains a challenge. Ujihara et al (2007 Appl. Phys. Lett. 91 093508) have recently proposed a thermo-magnetic energy harvester that incorporates a combination of hard and soft magnets on a vibrating beam structure and two opposing heat transfer surfaces. This design has many advantages and could present an optimum solution to harvest energy in low temperature gradient conditions. In this paper, we describe a multi-physics numerical model for this harvester configuration that incorporates all the relevant parameters, including heat transfer, magnetic force, beam vibration, contact surface and piezoelectricity. The model was used to simulate the complete transient behavior of the system. Results are presented for the evolution of the magnetic force, changes in the internal temperature of the soft magnet (gadolinium (Gd)), thermal contact conductance, contact pressure and heat transfer over a complete cycle. Variation of the vibration frequency with contact stiffness and gap distance was also modeled. Limit cycle behavior and its bifurcations are illustrated as a function of device parameters. The model was extended to include a piezoelectric energy harvesting mechanism and, using a piezoelectric bimorph as spring material, a maximum power of 318 μW was predicted across a 100 kΩ external load. © 2013 IOP Publishing Ltd.