A feedback control scenario of plasma burning in a tokamak reactor is investigated, whereby compression-expansion of the plasma provides routine control against small deviations from equilibrium, while occasional larger perturbations (expected to be of the cooling type only) are counteracted by the switching on of part of the additional heating system. The feasibility of the proposal is investigated on a profile-corrected zero-dimensional linearized model of the burning plasma, involving separate energy balances for electrons, ions, and alpha particles. Special attention is paid to control-theory features, with the aim to suitably interface them with plasma physics and fusion physics. A positive assessment concerning the feasibility of the proposed scheme is derived, with the proviso, however, that enough accuracy be obtained from the diagnostics that control the input to the feedback loop