Blackbody radiation sources are calculable radiation sources that are frequently used in radiometry, temperature dissemination, and remote sensing. Despite their ubiquity, blackbody sources and radiometers have a plethora of systematics. We envision a new, primary route to measuring blackbody radiation using ensembles of polarizable quantum systems, such as Rydberg atoms and diatomic molecules. Quantum measurements with these exquisite electric field sensors could enable active feedback, improved design, and, ultimately, lower radiometric and thermal uncertainties of blackbody standards. A portable, calibration-free Rydberg-atom physics package could also complement a variety of classical radiation detector and thermometers. The successful merger of quantum and blackbody-based measurements provides a new, fundamental paradigm for blackbody physics.