Temperature effects on Anodized Aluminum Parts

Look up the coefficient of thermal expansion for your aluminum alloy and for aluminum oxide. BIG difference and the hard anodize will probably crack and possibly delaminate.
If the inserted part is not anodized, look into shrinking it by using liquid nitrogen and rapidly press that part into a warm larger part. Wonderful shrink fit after they reach room temp.
Dry ice and alcohol get quite cold also, but not as much as liquid gasses and probably cost as much in the long run.
Safety measures are mandatory for both.

Sheasby and Pinner say, "fine cracks may be observed at 80-100C - - cracking is caused by the low coefficient of expansion of the anodic film which is approximately 0.2 times that of the metal,"