  We present the first $N$-body simulations that adapt the equations of
smoothed particle hydrodynamics to capture the effect of dark matter
self-interactions which are too frequent to be resolved explicitly. The
relevant energy transfer equations are derived, the appropriate thermal
conductivity is determined and the effects of different smoothing kernels are
studied. We apply our framework to simulate the formation of isothermal cores
in isolated dark matter haloes and determine the core growth rate as a function
of the self-scattering cross section. Our approach may be combined with
explicit simulations of rare scatterings in order to simulate accurately the
effects of arbitrary dark matter self-interactions in future cosmological
simulations.
