A scalable mapping system for superconducting RF (SRF) cavities is presented. Currently, it combines local temperature measurement with 3D magnetic field mapping along the outer surface of the resonator. This allows for the observation of dynamic effects that have an impact on the superconducting properties of a cavity, such as the normal to superconducting phase transition or a quench. The system was developed for a single cell 1.3 GHz TESLA-type cavity, but can be easily adopted to arbitrary other cavity types. A data acquisition rate of 500 Hz for all channels simultaneously (i.e., 2 ms acquisition time for a complete map) and a magnetic field resolution of currently up to 14 mA/m/μ0 = 17 nT have been implemented. While temperature mapping is a well known technique in SRF research, the integration of magnetic field mapping opens the possibility of detailed studies of trapped magnetic flux and its impact on the surface resistance. It is shown that magnetic field sensors based on the anisotropic magnetoresistance effect can be used in the cryogenic environment with improved sensitivity compared to room temperature. Furthermore, examples of first successful combined temperature and magnetic-field maps are presented.