  We consider a time-stepping scheme of Crank-Nicolson type for the heat
equation on a moving domain in Eulerian coordinates. As the spatial domain
varies between subsequent time steps, an extension of the solution from the
previous time step is required. Following Lehrenfeld \& Olskanskii [ESAIM:
M2AN, 53(2):\,585-614, 2019], we apply an implicit extension based on so-called
ghost-penalty terms. For spatial discretisation, a cut finite element method is
used. We derive a complete a priori error analysis in space and time, which
shows in particular second-order convergence in time under a parabolic CFL
condition. Finally, we present numerical results in two and three space
dimensions that confirm the analytical estimates, even for much larger time
steps.
