Advances in low-temperature techniques allow us to measure temperature with a precision approaching one part in 1011. Using an rf-biased Josephson-array voltage source, we can control the power dissipated in electric heaters to the same level. At this level of precision, the algorithm used for thermal control and its sensitivity to the non-white character of the input noise become important factors limiting the temperature stability of fundamental physics experiments. We consider the problem of measuring slowly changing data in the presence of both while noise and sudden, short noise spikes. Such data is obtained in high-resolution experiments in earth-orbit, where the thermometers are struck and heated by charged particles. We devise control schemes that improve upon traditional methods. Specifically, a proportional-integral/proportional controller has a better step response, and applying a Kalman filter to the input signal significantly decreases noise injected by the feedback loop. We also describe a new algorithm for spike removal that is robust and has a fixed worst-case execution time. It is significantly faster than the algorithm used in experiments previously flown in space.