We have built upon earlier innovations in paramagnetic susceptibility thermometry at low temperatures to develop a device with a noise level of 25 pK/root-Hz, and with a drift rate of less than one nanokelvin per day. These thermometers have been used to discover new phenomena near the superfluid transition in helium-4, including nonlinear heat flow, and in a different experimental configuration, a new self-organized critical (SOC) heat transport state. This SOC state supports a new temperature / entropy wave that propagates only against the heat flux that forces this self-organization to occur, even when the system has self-organized on the normal fluid side of the transition. I will first discuss the physics of this thermometer and the fundamental noise limits of thermometry, and then show how this improved measurement technique has provided surprising insight into the nature of this quantum phase transition driven away from equilibrium by a heat flux. A new control technique permits us to hold an absolute temperature stable to within a nanokelvin near 2.7 K over an indefinite period to time. This may provide a vast improvement in baseline stability in future radiometric measurements of the cosmic microwave background temperature and its anisotropy, which may advance the study of this far larger non-equilibrium quantum phase transition. This work has been sponsored by NASA through its Microgravity Fundamental Physics Discipline, and conducted collaboratively by the DX (UNM) and CQ (Caltech) groups, with support from JPL's Low Temperature Science and Technology Group.