Here is a trend of 11 & 55 I&Q, along with the EOM temperature and PSL RMTEMP signals. You can see that there is definitely some fringe-like behavior for monotonic changes in temperature. This is consistent with what I have seen on the gyro table in the past.
Some other notes:
We ought to get to the bottom of the fringing. The CTE of LiNbO3 is ~2 ppm/K, so given that the wavelength is on the order of 0.5 K, this is probably not caused by the etalon effect (2ppm/K * 0.5K * ~1cm << 1064nm).