Well since you already saw the red mark on her leg, i would assume she was telling the truth.
You didn't say when you did this client, but i would ask her to come in asap to see the burns for myself. Then you can advise her from there. E45 cream is one of the best for burns and should be kept in the fridge. Otherwise maybe she should see her GP. Definitely get a look or a photo if you think this woman is not being truthful.
Did you test the wax temperature on her or yourself? We always apply on our inner wrist as this is a sensitive area, so you'll know straight away if its too hot.
Maybe you should invest in a new wax pot. It sounds quite unusual that you have no temperature control or on/off switch. Without a dial, how can you change the temperature if it is too hot?
Keep in touch with her so she knows you don't take this situation lightly.
Good luck