Ok, that all sounds like good news! She may feel warm because a dog's normal temperature is higher than ours. They can normally be up to 102.5 degrees.
If she is alert, breathing normally,and the vomiting isn't continuing, you can continue to monitor at home. I have attached a link her to an article on managing vomiting at home:
So you want to wait 6 to 8 hours after she has vomited before offering her anything to eat or drink. If she needs to go out to potty, take her on a leash so she can't eat grass or anything else outside. Her tummy needs to rest. If she goes 6 hours with no vomiting, you can start offering her small amounts of water or preferably pedialyte/gatorade since she is so small and young and we don't want her blood sugar to drop every few hours- about 1 teaspoon per pound of her body weight each time. If you don't have pedialyte or gatorade you can make a little sugar water or honey water instead. If after this, she has no vomiting, then tomorrow morning you can offer her a very small amount of food such as white rice and boiled chicken breast. If she keeps this down you can continue giving small meals every few hours.
If at any point she becomes weak, starts vomiting again, has diarrhea with any blood, trouble breathing, pale gums, then she needs to get into the vet ASAP. This is especially important since she is so young and small, it is easier for her to get dehydrated.