  The Primordial Inflation Polarization Explorer (PIPER) is a balloon-borne
telescope mission to search for inflationary gravitational waves from the early
universe. PIPER employs two 32x40 arrays of superconducting transition-edge
sensors, which operate at 100 mK. An open bucket dewar of liquid helium
maintains the receiver and telescope optics at 1.7 K. We describe the thermal
design of the receiver and sub-kelvin cooling with a continuous adiabatic
demagnetization refrigerator (CADR). The CADR operates between 70-130 mK and
provides ~10 uW cooling power at 100 mK, nearly five times the loading of the
two detector assemblies. We describe electronics and software to robustly
control the CADR, overall CADR performance in flight-like integrated receiver
testing, and practical considerations for implementation in the balloon float
environment.
