  A recently suggested modified BCS (MBCS) model has been studied at finite
temperature. We show that this approach does not allow the existence of the
normal (non-superfluid) phase at any finite temperature. Other MBCS predictions
such as a negative pairing gap, pairing induced by heating in closed-shell
nuclei, and ``superfluid -- super-superfluid'' phase transition are discussed
also. The MBCS model is tested by comparing with exact solutions for the picket
fence model. Here, severe violation of the internal symmetry of the problem is
detected. The MBCS equations are found to be inconsistent. The limit of the
MBCS applicability has been determined to be far below the ``superfluid --
normal'' phase transition of the conventional FT-BCS, where the model performs
worse than the FT-BCS.
