Nanomechanical systems are generally embedded in a macroscopic environment where the sources of thermal noise are difficult to pinpoint. We engineer a silicon nitride membrane optomechanical resonator such that its thermal noise is acoustically driven by a spatially well-defined remote macroscopic bath. This bath acts as an acoustic blackbody emitting and absorbing acoustic radiation through the silicon substrate. Our optomechanical system acts as a sensitive detector for the blackbody temperature and for photoacoustic imaging. We demonstrate that the nanomechanical mode temperature is governed by the blackbody temperature and not by the local material temperature of the resonator. Our work presents a route to mitigate self-heating effects in optomechanical thermometry and other quantum optomechanics experiments, as well as acoustic communication in quantum information.