  This paper studies the approximate and null controllability for impulse
controlled systems of heat equations coupled by a pair (A,B) of constant
matrices. We present a necessary and sufficient condition for the approximate
controllability, which is exactly Kalman's controllability rank condition of
(A,B). We prove that when such a system is approximately controllable, the
approximate controllability over an interval [0,T] can be realized by adding
controls at arbitrary n different control instants
0<\tau_1<\tau_2<\cdots<\tau_n<T, provided that \tau_n-\tau_1<d_A, where
d_A=\min\{\pi/|Im \lambda| : \lambda\in \sigma(A)\}. We also show that in
general, such systems are not null controllable.
