Is the elevator without air conditioning a property problem?

No, it's a developer's problem that the elevator in the community doesn't have air conditioning, which has nothing to do with the property. The owner requests to install air conditioner in the elevator, and the air conditioner belongs to the owner. If there is a fault, the maintenance costs will of course be borne by the owners. If the air conditioner is installed by the elevator company or the property, the property or the elevator company is responsible for the maintenance costs caused by the failure.