As I interpret it, "hotting up" is purely metaphorical, and "heating up" is usually literal (though not always). You might heat up your cup of tea by putting it

As I interpret it, "hotting up" is purely metaphorical, and "heating up" is usually literal (though not always). You might heat up your cup of tea by putting it on the stove, for example, but you would hot it up by tipping in some cocaine, adding a little umbrella, and drinking it from a pyrex glass covered in glitter.