<p>In this paper, we deal with the global well-posedness of the solution to the initial-boundary value problem of a class of semilinear heat equations coupled with dynamical boundary conditions at three initial energy levels (subcritical, critical and supercritical), where a boundary dissipation term −∣<i>u</i>_<i>t</i>∣^<i>m</i>−2<i>u</i>_<i>t</i> of the linear (<i>m</i> = 2) or nonlinear (<i>m</i> &gt; 1 and <i>m</i> ≠ 2) cases appears on the boundary. First, we give a threshold condition for the global existence and finite-time blowup of the solution with subcritical and critical initial energy. Second, for the linear boundary dissipation (<i>m</i> = 2), by employing the weak dissipativity (antidissipativity) of the semiflow of the solution inside the stable (unstable) manifold, we derive several sufficient criteria for the global-in-time existence and finite-time blowup of the solution with supercritical initial energy. Then, by modifying the Nehari functional and introducing two new families of potential well structures, we generalize the aforementioned results to the superlinear case (<i>m</i> &gt; 2) of the boundary dissipation. Finally, via a similar approach to that of the superlinear case (<i>m</i> &gt; 2) by modifying the Nehari functional, we also obtain two sufficient conditions of the finite-time blowup of the solution in the sublinear case (1 &lt; <i>m</i> &lt; 2) of the boundary dissipation. The nature of this paper is to establish the variational structure for the linear or nonlinear boundary dissipation in dealing with the global well-posedness of the solution.</p>