Heat-driven engines are hard to realize in nanoscale machines because of efficient heat dissipation1. However, in the realm of spintronics, heat has been employed successfully-for example, heat current has been converted into a spin current in a NiFe|Pt bilayer system2, and Joule heating has enabled selective writing in magnetic memory arrays3. Here, we use Joule heating in nanoscale magnetic tunnel junctions to create a giant spin torque due to a magnetic anisotropy change. Efficient conversion from heat dynamics to spin dynamics is obtained because of a large interfacial thermal resistance at an FeB|MgO interface. The heat-driven spin torque is equivalent to a voltage-controlled magnetic anisotropy4,5 of approximately 300 fJ V-1 m-1, which is more than twice the value reported in a (Co)FeB|MgO system6,7. We demonstrate an electric microwave amplification gain of 20% in a d.c. biased magnetic tunnel junction as a result of this spin torque. While electric d.c. power amplification in spintronic devices has been realized previously8, the microwave amplification was limited to relatively small amplification gains (G = radiofrequency output voltage/radiofrequency input voltage) and has never exceeded 1 (refs 9-13). A magnetic tunnel junction driven by radiofrequency spin transfer torque using ferromagnetic resonance enabled a relatively large gain of G ≈ 0.55 (ref. 12). Furthermore, radiofrequency spin waves were tuned by the spin transfer effect14,15. The heat-driven giant spin torque in the FeB|MgO16,17 magnetic tunnel junction, which shows a large magnetization precession and resistance oscillation under a d.c. bias, overcomes the above limitations and provides a gain larger than 1.