A recently suggested modified BCS (MBCS) model has been studied at finite temperatures. We show that this approach does not allow the existence of the normal (nonsuperfluid) phase at any finite temperature (FT). Other MBCS predictions, such as a negative pairing gap, pairing induced by heating in closed-shell nuclei, and superfluid to super-superfluid phase transition are discussed also. The MBCS model is tested by comparing it with exact solutions for the picket fence model. 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.