It was recently discovered that inclusions and other types of inhomogeneities can be nondestructively detected by thermoelectric measurements in an entirely non-contact way by using high-sensitivity magnetometers to sense the weak thermoelectric currents around the affected region when the specimen is subjected to directional heating or cooling. This paper presents theoretical models capable of predicting the magnetic field produced by thermoelectric currents around inclusions under external thermal excitation. We investigated how the magnetic signal to be detected depends on (i) the relevant physical properties of the host and the inclusion, (ii) the size of the inclusion, (iii) the polarization of the magnetometer, (iv) the lift-off distance of the magnetometer from the specimen, and the (v) direction and (vi) strength of the external heating or cooling applied to the specimen. The presented analytical model is numerically evaluated for comparison to experimental results that were obtained by measuring the magnetic field produced by thermoelectric currents around surface-breaking spherical tin inclusions in copper under external thermal excitation for different lift-off distances between the sensor and the surface of the specimen. The diameter of the inclusions and the lift-off distance varied from 2.4 to 12.7 mm and from 12 to 20 mm, respectively. A fairly modest 0.7 °C/cm temperature gradient in the specimen produced peak magnetic flux densities ranging from 1 to 250 nT, that could be easily measured by a commercial fluxgate magnetometer. The experimental results were found to be in very good agreement with our analytical predictions.