A tenant asks a landlord to get a heating or a/c problem repaired, with no results, so the tenant calls a repair company for a service visit. Who pays the repair company?

This has to be done properly. The tenant needs to inform the landlord in writing that this problem needs to be fixed. The tenant gives the landlord a deadline by when it should be fixed. The tenant informs the landlord, in writing, that if its not fixed, the tenant will call a repair person and deduct the costs from their rent.

Unless the tenant has laid the groundwork, they will be responsible for the bill.