A simple temperature regulator for the 1-20K range that can be used with either a resistive or capacitive sensor is described. The former is useful for applications involving no applied magnetic fields, whereas the latter is essential when a strong field is present. When used with a resistive sensor, short-term and long-term stabilities of 0.1 and 1 mK, respectively, are easily achieved. When used with a capacitive sensor, the stability is determined by the sensor drift and is limited to 1 mK short-term and 3-5 mK long-term.