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The copper coax filter expands with temperature, the expensive
commercial units are made from materials with lower expansion rates.
I propose putting a small Peltier cell < 5 watts (heat
and cool) and a temperature sensor on the base of the coax and surround it with
a lot of foam.
An 8 pin micro does the fast start up ramp and the slow control
ramps needed at the designated temperature.
A similar scheme was used for a tuned laser diode in a -40C
to +80C ambient. I will have a play.