Confidence will show up in you more and more the more you practice. As you go through the postures a lot of things will come up, and you will feel and experience a lot. Most of which will feel very uncomfortable. Remember though that the more discomfort you endure, the bigger the benefits.
There is a saying that goes ‘the posture begins the moment you want to get out of it’. The thing in you that wants to get out of discomfort is the ego, or the mind if you will. The ego is also the place where fear exists and when you push through and weaken the ego’s pull and impact on you, the amount of fear and caring what other people think will shrink in you.
Because you experience so much and get through so many emotions during class you build emotional toughness which in turn makes you more resilient to being highly affected by what would and has normally scared you in your past. That’s how and why you gain confidence through hot yoga. This is talking from an experiential point of view.