  We consider the control problem for the generalized heat equation for a
Schroedinger operator on a domain with a reflection symmetry with respect to a
hyperplane. We show that if this system is null-controllable, then so is the
system on its respective parts and the corresponding control cost does not
exceed the one on the whole domain. As an application, we obtain
null-controllability results for the heat equation on half-spaces, orthants,
and sectors of angle $\pi/2$. As a byproduct, we also obtain explicit control
cost bounds for the heat equation on certain triangles and corresponding prisms
in terms of geometric parameters of the control set.
