Plasmonic nanostructures can significantly advance broadband visible-light absorption, with absorber thicknesses in the sub-wavelength regime, much thinner than conventional broadband coatings. Such absorbers have inherently very small heat capacity, hence a very rapid response time, and high light power-to-temperature sensitivity. Additionally, their surface emissivity can be spectrally tuned to suppress infrared thermal radiation. These capabilities make plasmonic absorbers promising candidates for fast light-to-heat applications, such as radiation sensors. Here we investigate the light-to-heat conversion properties of a metal-insulator-metal broadband plasmonic absorber, fabricated as a free-standing membrane. Using a fast IR camera, we show that the transient response of the absorber has a characteristic time below 13 ms, nearly one order of magnitude lower than a similar membrane coated with a commercial black spray. Concurrently, despite the small thickness, due to the large absorption capability, the achieved absorbed light power-to-temperature sensitivity is maintained at the level of a standard black spray. Finally, we show that while black spray has emissivity similar to a black body, the plasmonic absorber features a very low infra-red emissivity of almost 0.16, demonstrating its capability as selective coating for applications with operating temperatures up to 400°C, above which the nano-structure starts to deform.