  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 thermal 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.
