Colpitts oscillator: how to reduce amplitude thermal drift?
The voltage offset of the amplifier is changing as well as most of your components. Make sure they all have low temperature coefficient's.

 

Another problem with the Colpitts oscillator is the use of magnetic elements, they must be properly shielded (which can be difficult with magnetic fields.)

This might be a better oscillator. I've seen them used in high stability applications. use low TC resistors, a low TC amp and a polypropylene capacitor.  There are much less components to worry about (and less TC's) and much less interference from magnetic noise. 



Another problem with either oscillator is the capacitors, capacitors can act like microphones and pick up vibrations, polyproplene capacitors are less susceptible to this effect.