Heat-driven engines are hard to realize in nanoscale machines because of efficient heat dissipation(1). 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 vertical bar Pt bilayer system(2), and Joule heating has enabled selective writing in magnetic memory arrays(3). 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 vertical bar MgO interface. The heat-driven spin torque is equivalent to a voltage-controlled magnetic anisotropy(4,5) of approximately 300 fJ V-1 m(-1), which is more than twice the value reported in a (Co) FeB vertical bar MgO system(6,7). 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 previously(8), 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 approximate to 0.55 (ref. (12)). Furthermore, radiofrequency spin waves were tuned by the spin transfer effect(14,15). The heat-driven giant spin torque in the FeB vertical bar 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.