The Space Interferometry Mission (SIM) has some very tight stability requirements that drive the thermal control approach well beyond the traditional spacecraft thermal control regime. The precision support structure will be constructed of composite materials with a quite low coefficient of thermal expansion (CTE) on the order of 10-7/K. Even then, the temperature variations of the structure cannot exceed about 0.2°C. For the main optical elements, which will be fabricated of ultra-low expansion glass, the temperature stability must be such that the temperature gradient through the glass cannot vary by more than a couple of millikelvin through the 5 cm thickness over a one hour period. The laser metrology system, which measures motions on the order of a few tens of picometers, contains some sensitive optical elements whose temperature variations cannot exceed a few tens of microkelvin. This paper will describe how the SIM thermal control designers have addressed some of these very challenging requirements.