We present a facile organic phase synthesis method for producing multi-branched gold nanocrystals (nanostars) with a broad localized surface plasmon resonance (LSPR) across near-infrared (NIR) to short-wave infrared (SWIR) wavelengths. In this approach, galvanic replacement of copper by gold, in seed particles produced in situ, initiates growth of multi-branched structures. The method enables broad tuning of the LSPR energy by manipulating the branch length, with peak LSPR absorbance tuned from 850 to 1880 nm, reaching SWIR wavelengths covering the second and third optical transparency windows in biological media, rarely achieved with noble metal plasmonic nanostructures. After a ligand-exchange process, the gold nanostars readily disperse in water while retaining their LSPR absorbance. The multi-branched Au nanocrystals (NCs) exhibit exceptionally high photothermal transduction efficiency, exceeding that of Au nanorods and nanoparticles, to which we make direct comparisons here. At the same time, their synthesis is much more straightforward than hollow structures like nanocages, nanoshells, and nanomatryoshkas that can also exhibit high photothermal efficiency at NIR wavelengths. In vitro photothermal heating of multi-branched Au NCs in the presence of human cervical cancer cells causes effective cell ablation after 10 min laser irradiation. Cell viability assays demonstrate that the NCs are biocompatible at doses required for photothermal therapy. These results suggest that the multi-branched Au NCs can serve as a new type of photothermal therapy agent and in other applications in which strong NIR to SWIR absorbers are needed.