You have a very kind heart. If you think the bunny is cold, a little warm water to drink would not hurt. Rabbits under stress can exhibit shaking, but hopefully it will settle down when it feels safe. Sounds like you are already there. Assuming the bunny makes it through the night, he will probably do very well with some good rabbit pellets and TLC from you.
If money is not a concern, then maybe a vet visit is in order. However, for many of us, a vet visit is not an option. As I have said, I can buy 20 healthy chicks for the price of one visit to the vet for a sick chicken - and our local vets don't treat poultry anyway. But they will charge you for a visit just the same.
Sometimes the local farm store has people who have knowledge on raising small animals and might to be able to give you some good advice on treatment options and even have the medicine in the store. I know my local farm store has people that have been raising chickens for 20+ years, so their advice is always considered.
Keep this thread updated as I would like to hear a happy ending. Best wishes.