I don't mean that you would be paid as such for doing extra chores, but that you would be contributing more towards the running of your home and instead if payment, your parents could overlook the extra heating/lighting bills from keeping your tort :)
If your parents are anything like mine...
Have you tried explaining to your parents that you would rather give him away to a good home, than not be able to give him the minium care he needs?
Could you offer to do any more chores for your parents in order to help towards the heating costs?