I’m mellow but hot and 72+ would put me in battle mode. 61 would feel great to me but that is unreasonable for a shared space, as is 72+ for a hot natured person. Maybe try 67-68.
BTW- I grew up and attend school in Miami. We kept the a/c on in the dorm room year round.
I think 72 is a perfectly fine temperature; 70 is okay, but anything less would make my bones cold and I’d find it impossible to concentrate. You can’t work when you can’t feel your fingers and toes.
You two are incompatible temperature wise. You’re paying for the room too, so change the thermostat as often as you want. If you can’t find a middle ground that works for both of you then see if you can switch rooms.
All this is why I’m a huge advocate of solo dorm rooms (cleaned by student) and old-style community bathrooms (cleaned by staff).
***Update: It was 61 degrees outside last night, and my roommates had the air at 65. It literally felt like the artic. My teeth were chattering.
I feel your pain. It wasn’t nice of her to tell you that you couldn’t touch the thermostat. That said, I’m usually the one who is cold, and my husband is always hot. I can generally make myself comfortable by wearing soft wool sleep socks and warmer PJs at night, and wearing a sweatshirt or sweater during the day. I also have an electric throw blanket when he gets impossible. From his viewpoint, I can easily fix my feeling cold by throwing on an other layer. Once he is too hot, he can’t easily find relief in the room. I accept that and I’m the one who makes the compromise.
I hope you find a solution that works for both of you. This one is is pretty common!
65 is an icebox. When I go on vacation during the winter, I set the thermostat to 65, just to keep the house at some basic minimum level. Sorry, I’d crank it up to 68-70, stand in front of the thermostat, and say “come at me bro.” 
Did you turn the heat up? She can’t stop you from touching the thermostat.
I did turn the air up. But I was so afraid to because I was afraid she would snap at me and yell at me for turning the air up like she always does.
I had a foreign roommate when I was a sophomore that always cooked curry my only was I could survive was to constantly spray axe to cover the smell good luck!
Instead of dreading her snapping at you, perhaps you can role play with a friend how you will calmly respond when that inevitably occurs. Living in fear of someone else’s rage is never a good idea. Somewhere along the line you will have someone else who will try to bully you (very possibly a work colleague). So, learning to be assertive without lashing out and destroying the relationship is a great skill to have in your back pocket for the future.