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We propose a novel type of sensor where the sensitive element is an isolated, passive absorber of extremely low thermal mass, maintained close to its superconducting-normal transition, and strongly inductively coupled to a SQUID sensor. Incoming particles or photons are sensed in terms of a transient change in the inductive coupling, rather than a change in resistance. Energy sensitivity and response time can then be defined by the thermal mass of the absorber and its thermal contact with a substrate, independently of any electrical connections. An ultimate energy resolution of order 10-25 J/Hz is theoretically estimated, based on the properties of the SQUID and the dimensions of the absorber. Calculations of the thermal properties of the absorber suggest that a response time of 1 ns should be feasible, although in practice this will be limited by the bandwidth of the SQUID amplifier. Proof-of-principle measurements on a prototype device are presented, where a SQUID flux noise level of 4×10-7 fluxon/Hz1/ was achieved and laser-induced superconducting-normal transitions of a thin-film Pb-Sn absorber were clearly demonstrated.