Hi,
CAG's as with any bird adjust to the temperature where they live.. the only time a problem could occur is if a bird is taken out of a very warm area and placed in to extreme cold or vica versa. i've 3 birds here who were previously house birds but due to their needs they now live outdoors. They have adjusted to the temp change over the months and despite temps of down to -6 none of them have suffered any problems. Infact i have even gone out in the morning to find them bathing in the icy water!!!
The downside is that because this birdie is used to the cooler temps if/when he gets a new home he could have problems acclimatsing to a 'normal' heated home ie he could over heat, suffer with dry /itchy skin etc.
Provided he is a healthy bird and has all that he needs in the way of food/ housing etc then i don't see there is any major concern. Someone else may disagree, this is only my opinion going by the experience i've had but i hope it helps ease your concerns.
shaz