I have two of these, they come in two sizes. They are exactly what you want. They are slightly narrow, you can bend your cage in or use a cheap thin bottle cozy from something else. They are made for hot beverages and work great one handed. I've tired them all this is by far the best for hot drinks on the roll.

http://www.techbooksunlimited.com/i/item_B00025DYL0.php


From Thermos on line too. Take a look.