If the new viv isn't heated, putting the Faunarium in it won't help a whole lot. If your room doesn't get below about 70*F, the new viv should be okay with no heat until you get it. Just don't feed the snake that gets moved until the new viv has heat. If you're worried about heat, you may be better off leaving them together in the Faunarium until you can get heat on the new viv.
Come to think of it, putting the Faunarium in the new viv may be a burn risk. Even if you have a thermostat (which you should), the heat pad itself is going to be hotter than the inside of the Faunarium where it touches. If the snake gets under it, you risk it getting burned... Again, considering this, you're better leaving the new viv unheated or leaving them together (depending on your room's ambient temps).