If your heating system is faulty, you should first check the simple causes: Is the thermostat set correctly? Is the power supply working? Is the pressure on the heating pressure gauge in the green range? Restarting the heating by pressing the reset button often helps.
As a tenant, you are obliged to report the defect to your landlord or property management company immediately - preferably in writing. The landlord must arrange for the repair, whereby in the event of an acute heating failure in winter, a period of 24 hours applies for the repair if health is at risk (e.g. due to the risk of frost in the flat). As the owner, you should contact a certified heating engineer or the manufacturer. Many companies in Dresden offer emergency services. You can find an overview on the website of the Dresden Chamber of Crafts under the keyword "Heating".
If the repair takes longer or the heating system is outdated, it may make sense to replace it. Take the opportunity to think about climate-friendly alternatives such as heat pumps or district heating. The Energy Pilot of the City of Dresden can help you with this. Funding opportunities for modern heating systems are offered by KfW and BAFA, among others. You can find a comprehensive overview here. In the event of financial difficulties or acute danger of cold, you can contact the social welfare offices of the city of Dresden or Caritas. If carbon monoxide is suspected (e.g. in the case of defective gas heating systems), leave the room immediately, ventilate and alert the fire brigade by dialling 112 or the chimney sweep emergency service on 0351 488 8888.