  CrSb is an attractive material for room-temperature antiferromagnetic
spintronic applications because of its high N\'{e}el temperature $\sim$700 K
and semi-metallic character. We study the magnetic properties of CrSb bilayers
on few-layer topological insulator thin films using \emph{ab initio} density
functional theory. We find that the intrinsic parts of the total anomalous Hall
conductivities of the thin films are non-zero, and approximately quantized. The
N\'{e}el temperature of CrSb bilayers on few-layer topological insulator thin
films is found to be approximately two times larger than that of an isolated
CrSb thin film. Due to the low Fermi level density of states of CrSb, Hall
quantization might be achievable by introducing disorder. CrSb bilayers on
topological insulator surfaces are therefore attractive candidates for
high-temperature quantum anomalous Hall effects.
