jats:titleAbstract</jats:title>jats:pSpin thermo-electric phenomena have attracted wide attention recently, e.g., the spin Peltier effect—heat generation by magnonic spin currents. Here, we find that the spin Peltier effect also manifests as a heat wave accompanying fast moving magnetic textures. High speed and extreme magnetic excitation localisation are paramount for efficient transfer of energy from the spin-degrees of freedom to electrons and lattice. While satisfying both conditions is subject to severe restrictions in ferromagnets, we find that domain walls in antiferromagnets can overcome these limitations due to their ultrahigh mobility and ultra-small widths originating from the relativistic contraction. To illustrate our findings, we show that electric current driven domain wall motion in the antiferromagnetic metal Mnjats:sub2</jats:sub>Au can carry a localised heat wave with temperature up to 1 K. Since domain walls are localised magnetic objects, this effect has the potential for nanoscale heating sensing and functionalities.</jats:p>