  We consider the space-time boundary element method (BEM) for the heat
equation with prescribed initial and Dirichlet data. We propose a residual-type
a posteriori error estimator that is a lower bound and, up to weighted
$L_2$-norms of the residual, also an upper bound for the unknown BEM error. The
possibly locally refined meshes are assumed to be prismatic, i.e., their
elements are tensor-products $J\times K$ of elements in time $J$ and space $K$.
While the results do not depend on the local aspect ratio between time and
space, assuming the scaling $|J| \eqsim {\rm diam}(K)^2$ for all elements and
using Galerkin BEM, the estimator is shown to be efficient and reliable without
the additional $L_2$-terms. In the considered numerical experiments on
two-dimensional domains in space, the estimator seems to be equivalent to the
error, independently of these assumptions. In particular for adaptive
anisotropic refinement, both converge with the best possible convergence rate.
