We demonstrate radio-frequency thermometry on a micrometer-sized metallic island below 100 mK. Our device is based on a normal-metal–insulator–superconductor tunnel junction coupled to a resonator with transmission readout. In the first generation of the device, we achieve 90 μK/√Hz noise-equivalent temperature with 10 MHz bandwidth. We measure the thermal relaxation time of the electron gas in the island, which we find to be of the order of 100 μs. Such a calorimetric detector, upon optimization, can be seamlessly integrated into superconducting circuits, with immediate applications in quantum-thermodynamics experiments down to single quanta of energy.