Yes, there are several ways of saving money on a heating bill, from scheduling heating maintenance to increasing the efficiency of the system; anything can be practised, which in turn helps in reducing the energy bills. It is a must to ensure that the system is clean and the filters are being changed regularly.
If the heating bill does not reduce even after trying all the options, it is wise to replace the system. It will save a lot of money and will heat the space more effectively.