Atomic force microscopy (AFM) experiments were performed to study the behaviour of AFM cantilevers under an external magnetic field B and temperature field produced by a coil with an iron core. Four cantilever types were studied. Forces were measured for different B values and at various coil-to-cantilever separation distances. The results were analysed on the basis of a phenomenological model. This model contains the contribution of two terms, one monopole-monopole interaction at short distance, and one apparent paramagnetic interaction in del B-2 at large distance, which represents the temperature effects. We observe a good agreement between the model and the experimental data.