As stated in the comments, 6 weeks is a little bit too young to get separated from her mother. Taking the puppy away from her mother after 8 weeks would be more preferable. But now it happend and so it will be at bit harder for you to train her to be left alone, because she misses her family.
Be together with her as much as you can. Don't let her alone if it is not really needed. Play with her, train her (yes it is possible to start with training in such a young age, but be patient with her and don't require too much), so that she is tired when you have to leave her alone for a short while. Huggle together often. But keep in mind that young dogs are tired very soon, so give her time to relax.
Give her some stuffed animals, which preferably are bigger or the same size as your puppy. She will feel less lonely.
Giving her a hot water bottle was a good idea. Keep on with it, but remind that it should not be too hot. It should not hurt her.
To train that she can be left in the crate, play with her to make her tired. Than put her in it, wait for half a minute and take her out of it before she starts crying. Pet her for a little while and than put her in it again. Observe her. Does she wants to sleep? Very good. Let her sleep for a while. If you see that she wakes up, take her out of the crate before she is really awake and starts crying. Try not to leave the room for the first training sessions. Try to extend the time of leaving her in the box.
Then try to leave the room while she is in the crate. Even if she accepts staying in the crate while you are in the same room for longer than 10 minutes without crying that does not mean that you can leave the room for 10 minutes. So start with half a minute first. Extend the time of your absence.
It may be a good idea to keep her in the same room at night for the next few weeks. It is possible to change that later. But keep in mind that she is really young and feels lonely. And you should not leave her alone for the whole day. She is definetly too young for that.