On a national level, Sweden has announced plans to have no net emissions of greenhouse gases in 2045. Furthermore, Gothenburg, a city in southwestern Sweden, has plans to phase out the use of fossil fuels in its heat and electricity production by 2030. Given that the development of a district heating (DH) system under dynamic and different climate policies and climate goals is a nontrivial problem, this study investigates two different policies of phasing out fossil fuels, either by introducing a fossil fuel ban, or by increasing the carbon tax to phase out the fossil fuel use in 2030 or 2045. The effects of the different phase out strategies on the future development of the existing DH system in Gothenburg has been investigated. The study is based on a system-wide approach covering both the supply and demand side developments. A TIMES cost optimizing energy system model representing the DH system of Gothenburg was developed and applied for calculations. The results show that the total amount of heat supplied by the DH system is unaffected by the phase out policies. The amount of natural gas used to supply the DH system is however dependent on what kind of phase out policy is implemented. A yearly increasing carbon tax policy introduced in 2021 phases out fossil fuel use earlier than the target year, while a ban phases out the fossil fuel only from the actual target year.