  Recent observations have found a growing number of hypervelocity stars with
speeds of $\approx 1500-2500\,$km\,s$^{-1}$ which could have only been produced
through thermonuclear supernovae in white dwarf binaries. Most of the observed
hypervelocity runaways in this class display a surprising inflated structure:
their current radii are roughly an order of magnitude greater than they would
have been as white dwarfs filling their Roche lobe. While many simulations
exist studying the dynamical phase leading to supernova detonation in these
systems, no detailed calculations of the long-term structure of the runaways
have yet been performed. We use an existing \textsc{Arepo} hydrodynamical
simulation of a supernova in a white dwarf binary as a starting point for the
evolution of these stars with the 1 dimensional stellar evolution code MESA. We
show that the supernova shock is not enough to inflate the white dwarf over
timescales longer than a few thousand years, significantly shorter than the
$10^{5-6}$ year lifetimes inferred for observed hypervelocity runaways. Despite
experiencing a shock from a supernova less than $\approx 0.02\,R_\odot$ away,
our models do not experience significant interior heating, and all contract
back to radii around $0.01\,R_\odot$ within about $10^4$\,years. Explaining the
observed inflated states requires either an additional source of significant
heating or some other physics that is not yet accounted for in the subsequent
evolution.
