  We present the first implementation of hyperbolic thermal conduction in
smoothed particle hydrodynamics (SPH). Hyperbolic conduction is a
physically-motivated alternative to traditional, parabolic conduction. It
incorporates a relaxation time, which ensures that heat propagates no faster
than a physical signal speed. This allows for larger, Courant like, time steps
for explicit schemes. Numerical solutions of the hyperbolic conduction
equations require added dissipation to remain stable at discontinuities and we
present a novel scheme for this. Test cases include a simple step, the Sod
shock tube, the Sedov-Taylor blast, and a super bubble. We demonstrate how
longer relaxation times limit conduction, recovering the purely hydrodynamical
results, while short relaxation times converge on the parabolic conduction
result. We demonstrate that our scheme is stable with explicit Courant-like
time steps and can be orders of magnitude faster than explicit parabolic
conduction, depending on the application.
