It may, as taking a hot bath will somewhat. But training in a hot room can be dangerous. You don't say what kind of training, so I'm assuming it might be yoga?
No, but exercise alone stimulates the pituitary gland to release HGH.
The best way to increase HGH while training is through interval training.
Pair up an aerobic exercise and an anaerobic exercise and your body will not only increase the amount of growth hormone produced, but it will also build muscle and burn more fat.
I have found no evidence that this happens during hot yoga.