We introduce a microwave bolometer aimed at high-quantum-efficiency detection of wave packet energy within the framework of circuit quantum electrodynamics, the ultimate goal being single microwave photon detection. We measure the differential therma
l conductance between the detector and its heat bath, obtaining values as low as 5 fW/K at 50 mK. This is one tenth of the thermal conductance quantum and corresponds to a theoretical lower bound on noise-equivalent-power of order $10^{-20}$ $W/sqrt{mbox{Hz}}$ at 50 mK. By measuring the differential thermal conductance of the same bolometer design in qualitatively different environments and materials, we determine that electron--photon coupling dominates the thermalization of our nanobolometer.
