Does the property have the right to turn off the heating privately?

No, the heating policy is a local regulation. Take Beijing as an example:

"Beijing heating management measures" fifteenth heating period, the heating unit shall not postpone, suspend or end the heating ahead of schedule, and shall not withdraw or partially withdraw from the heating business activities; Units that supply water, electricity, gas, fuel oil, coal and heat energy to heating units shall ensure the supply and shall not interrupt without authorization.

During the non-heating period, if the heating unit really needs to withdraw or partially withdraw from the heating business activities, it shall properly arrange the related users, facilities management and protection, heating costs and other matters within the heating range, and complete the handover of heating facilities and technical files, user information, heating costs and other matters with the undertaking heating unit before July 15 of that year, and inform the original filing organ in writing at the same time.

When the heating rights and interests of users cannot be effectively guaranteed, the heating unit shall not withdraw or partially withdraw from the heating business activities.

The extended data heating unit is responsible for the management, maintenance, repair and transformation of outdoor heating facilities and indoor heating facilities for residents within the heating range. The logistics service departments of organs, military units, enterprises and institutions can entrust professional enterprises to undertake social heating services in accordance with regulations.

When residential users find that the indoor heating facilities are abnormal and leaking, they shall promptly report to the heating unit for repair, and bear the relevant expenses for the maintenance and renewal of indoor self-use heating facilities. The maintenance, management and transformation of heating facilities for non-resident users shall be agreed in the contract between the heating unit and the users. The construction unit shall bear the warranty responsibility of heating facilities in accordance with the law during the warranty period.

Beijing Municipal People's Government-Measures of Beijing Municipality on the Administration of Heating