  In this paper we study the boundary behavior of solutions of a
divergence-form subelliptic heat equation in a time-varying domain \Omega in
R^{n+1}, structured on a set of vector fields X = (X_1, ... X_m) with smooth
coefficients satisfying H\"ormander's finite rank condition. Assuming that
\Omega is an X-NTA domain, we first prove a Dahlberg type estimate comparing
the X-caloric measure of \Omega and the Green function of the subelliptic heat
operator. We then prove a backward Harnack inequality, the doubling property
for the X-caloric measure of \Omega, the H\"older continuity at the boundary
for quotients of solutions of H, and a Fatou theorem.
