  We derive optimal order a posteriori error estimates for fully discrete
approximations of the initial-boundary value problem for the heat equation. For
the discretization in time we apply the fractional-step $\vartheta$-scheme and
for the discretization in space the finite element method with finite element
spaces that are allowed to change with time. The first optimal order a
posteriori error estimates in $L^\infty(0, T ; L^2({\varOmega}))$ are derived
by applying the reconstruction technique.
