  We report on noise and thermal conductance measurements taken in order to
determine an upper bound on the performance of graphene as a terahertz photon
detector. The main mechanism for sensitive terahertz detection in graphene is
bolometric heating of the electron system. To study the properties of a device
using this mechanism to detect terahertz photons, we perform Johnson noise
thermometry measurements on graphene samples. These measurements probe the
electron-phonon behavior of graphene on silicon dioxide at low temperatures.
Because the electron-phonon coupling is weak in graphene, superconducting
contacts with large gap are used to confine the hot electrons and prevent their
out-diffusion. We use niobium nitride leads with a $T_\mathrm{c}\approx 10$ K
to contact the graphene. We find these leads make good ohmic contact with very
low contact resistance. Our measurements find an electron-phonon thermal
conductance that depends quadratically on temperature above 4 K and is
compatible with single terahertz photon detection.
