Am I reading something no one else is? The snake is over twice the length of the tub? I think a slightly bigger tub would be a good thing, also would help in making sure it doesn't overheat. A 14 inch long tub is practically a shoebox, and I think(IMO) that a 31 inch long snake has outgrown it.

The best is to use either a thermostat or at least a dimmer switch on your heatmat.

Most likely she will calm down, but even if she did manage to bite you, it's not a big deal. Just get it over with, and you'll laugh at yourself for being worried. When reaching in, you can use a piece of paper to shield your hand, so the snake doesn't see "Giant hand o doom" coming at it. Once you've picked her up, she should be fine.