I went through the same dilema as you!
My family and I were going to Tasmania for a holiday, and as we live in New South Wales, the only way there was by boat or plane. I couldn't stand to leave my little budgie in the care of someone else for 3 weeks so he had to come with us. My budgie survived a 12 hour boat trip in our car in the car area of the boat which just above the water level with no heating other than the heat that was in the car, and he was fine
So I believe that you little birdy should be fine.
A hot water bottle underneath the cage and a warm cover should be alright... perhaps you could run a battery run heater?
I wish you best of luck.
Budgies are one tough little birds, try not to worry too much!
