Heat bullets

New localized structured solutions for the three-dimensional linear diffusion (heat) equation are presented. These new solutions are written in terms of Airy functions and either Gaussian or Bessel functions. They accelerate along their propagation direction, while in the plane orthogonal to it, they retain their either Gaussian or Bessel structure. These diffusion (heat) densities retain a localized structure in space as they propagate, and may be considered the heat analogue of Airy light bullets.