What would worry me is the effect of wavefront error caused by temperature differences across the plate. Lets take alpha=7.1*10^-6/K, index n = 1.517 (i.e. BK-7). Consider light passing through a thickness a of glass followed by thickness b of air. Light with wavelength l in air has wavelength l/n (I think) in glass so the path length is (an+b)/l wavelengths.
Now make the glass thicker by d. Path length becomes ((a+d)n + b-d)/l wavelengths, i.e. (n-1)d/l wavelengths more. Say we want to limit this to 1/8 wave, l = 22*10-6 inch then d<=5.3*10-6 inch. If I want an optical window 0.5" thick I must not have a peak to peak variation of temperature within it of more than 1.5 K. (NB: this assumes that refractive index does not change with temperature, I'm not sure about this).
Now this seems to be a tall order in a window of any size: sideways heat conduction will be very slow, so it will only stay at a uniform temperature throughout if whatever cools it during the night acts uniformly across it. One might need a "stirrer" within the tube that could be switched on from time to time to blow air over it and even out the temperature!
Has anybody any experience of this effect? Is it actually a problem? Does refractive index change with temperature and cancel out the wavefront errors?
Roger Moss