This paper presents sufficient conditions for dispersiveness of linear control systemns on the Heisenberg group. The dispersiveness implies the absolute stability of the orbits, which means stability of all orders. Necessary conditions for the existence of a control set are derived. A linear control system is determined by a derivation D of the Heisenberg algebra h and invariant vector fields X₁,…,X_{m}. The main result assures that the system is dispersive with respect to a compact set K in the control range, if the mean limits lim(1/(t_{n}))∫₀^{t_{n}}∑u_{i}ⁿ(s)X_{i}ds do not reach the subspace h²+Im(D)⊂h. Consequently, the system is K-dispersive, if 0∉K and the sum h²+Im(D) meets Span{X₁,…,X_{m}} trivially. The mean limit criterion is applied to the linear Heisenberg flywheel and other three-dimensional systems.