I have had to transport in cold weather and I warm the car up first, then place my carrier in the front seat and buckle it in and then put a nice heavy blanket over the carrier as well. Also you can warm a blanket for the inside of the carrier in a clothes dryer, just be careful that the blanket is not too hot when you put Cassie in it.

I have also used a hot water bottle underneath a blanket to keep a cat warm.