  We study the small-time asymptotics of the relative heat content for
submanifolds in sub-Riemannian geometry. First, we prove the existence of a
smooth tubular neighborhood for submanifolds of any codimension, assuming they
do not have characteristic points. Next, we propose a definition of relative
heat content for submanifolds of codimension $k\geq 1$ and we build an
approximation of this quantity, via smooth tubular neighborhoods. Finally, we
show that this approximation fails to recover the asymptotic expansion of the
relative heat content of the submanifold, by studying an explicit example.
