Each council has its own rules. You will need to check with your local council. Currently, Multi fuel units are allowed in Auckland, Hamilton, Wellington that I know of, although the rules are always changing. Generally, if you are out of clean air zone and over 2ha they are allowed. You do have the option of going for a resource consent if you are in other areas.
This is not ideal. What happens is that the hot air pulls the cold air through, creating draughts throughout your house. It is best to have a radiator in each space. This is how you achieve a constant temperature throughout the home.