Does the property have the obligation to collect heating fees for the heating company?

Without this obligation, you can accept the entrusted service, but the actual situation is that you have offended the heating company and the owner is not happy if the heating is not timely.

Article 45 of the Detailed Rules for the Implementation of the Property Management Regulations

Within the property management area, water supply, power supply, gas supply, heating, communication, cable TV and other units shall charge relevant fees to the end users. If a property management enterprise accepts the entrustment to collect the fees mentioned in the preceding paragraph, it shall not collect additional fees such as handling fees from the owners.