A breast tumor is visible by a passive microwave radiometer if it changes the radiometric output of a healthy breast to an extent that overcomes the radiometric resolution for the given sensing antenna and integration time. We modeled breast temperature by the standard Pennes equation using thermal parameters found in the literature for normal and cancerous breast tissue. An apparent thermal volume and its dependence on blood perfusion have been estimated. The radiometric weighting function has been evaluated as a function of the size of a contacting antenna modeled as an aperture antenna. For comparison with the radiometric resolution, the difference signal between the outputs in the presence of a lesion and in its absence has been evaluated for different tumor sizes and depths. The results of the numerical analysis show that this difference signal depends on the average over-temperature in the lesion times the heating efficiency, given by the fraction of power delivered to the tumor when the antenna radiates onto the breast in active modality. A tumor of 6 mm (10 mm) diameter is visible by a 0.1 K radiometer and a 3 cm aperture antenna when it is not deeper than 1.2 cm (2.8 cm) under the assumption of ideal radiometer and antenna.