I will say a towel and the pillow case is still the quickest was but I would leave a travel cage near to him. I could of had a fire if I had not noticed wires bitten through by my birds but also I have lost my two Parrot finches after the heated cage developed an electrical fault. I was lucky that it did not affect other birds in the room and that the fuse tripped and no fire had started. My home is mainly wood and fire can be a major concern I have a very good alarm set up that was installed by the fire brigade. it would be very difficult to evacuate the birds in there cages from the bird room and the only way out apart from going through my whole bungalow is via a small double window. I have fire extinguish in most rooms and fire blankets standing by.