The Subtleties of Bird Shipping?

 
The Subtleties of Bird Shipping?
We're moving, and traveling to our new home by plane. It will be in the winter, and we don't want our parakeet to get too cold or sick. The coldest it would be outside is like in the 30's, and we'll have him in a small travel cage and that rapped in a heavy blanket to keep out any cold wind if there is any. It's just that we fear any sudden temp changes could get him sick. So is this a concern as long as we keep him rapped or are there any warming things we can put in the carrier or anything for shipping we don't know about?We're not shipping him, but it could work the same way. He's being carried on the plane by me and put under my seat as I want to keep him close. Just want to know if there is anything else I should do.
I think covering him with a fleece blanket would work well enough. Birds can naturally regulate their temperatures pretty well, and I've talked to people who have conditioned their birds live in an out door, only partially heated aviary all year long, and it can get 30 degrees or colder in his aviary.