We observe amplification of spin-wave packets propagating along a film of single-crystal yttrium iron garnet (YIG) subject to a transverse temperature gradient. The spin waves are excited and detected with standard techniques used to study volume or surface magnetostatic waves in the 1–2 GHz frequency range. Amplification gains larger than 20 are observed in a YIG film heated by a current of 20 mA in a Pt layer in a simple YIG/Pt bilayer. The amplification is attributed to the action of a spin-transfer thermal torque acting on the magnetization that opposes the relaxation and which is created by spin currents generated through the spin Seebeck effect. The experimental data are interpreted with a spin-wave model.