We propose an rf-SQUID microcalorimeter in which the critical current of a Josephson junction can be varied by an electron temperature in the normal metal barrier of the superconductor–normal metal–superconductor or superconductor–normal metal–insulator–superconductor junctions. In this detector, a Josephson junction with a radiation absorber is included in a superconductor loop and the change of its critical current is converted into a change of the terminal voltage of a tank circuit. We estimated the energy resolution of this detector by calculating the noise equivalent power of the detector. The estimated energy resolution is 1.5 eV with an Ag absorber of 500 × 500 × 2 µm3 at 100 mK.