My teacher always says that you always perform worse a lesson than at your home
A good teacher with enough experience should know this and always take in account the "not on your home, not in your piano, in front of your teacher" factor
I know even at the exam they take this clearly into account
If you become sweety the solution is to stand up, breath at the windows and drink a glass of water every other piece
If you keep seating for 60 minutes without breathing, stretching, drinking and walking will you lose your concentration and calm very soon
In fact if you want to be a concertist you need to train your endurance, but it's not needed at your lesson
I've noticed that if I stand up and stretch between performing my pieces for few seconds I play a lot better when I come back to the piano
Always perform your lesson with the windows open, you need lot of oxygen
Don't forget also to be comfortable with what you dress, not heavy fleece or sweaters just a short sleeve t-shirt so that you don't get too hot and sweety
Daniel