If your home heating and cooling system stops working and you live in a rented house, you should try to keep the following two tips in mind.
Do not try to fix it without your landlord's help
In this situation, it would be unwise to take on the repair of the broken heating and cooling system by yourself or to hire a cheap tradesperson with no experience in HVAC systems to fix it. Rather than doing this, you should call your landlord and have them pick a HVAC contractor of their choosing, who can then come to your house and fix the system.
The reasons for this are as follows; firstly, if your amateurish efforts to repair the system lead to additional damage (for example, if you break the vent when trying to remove it so that you can examine the internal components), your landlord might charge you a fee to get this damage resolved.
Secondly, if you decide not to notify your landlord, but to instead hire a general tradesperson who does not specialise in fixing HVAC systems, simply because they charge so little for their services, and this tradesperson makes a major error that leaves the system broken beyond repair, your landlord might not be able to use their HVAC warranty to cover the cost of getting the system replaced, because the 'repairs' were not done by a HVAC contractor (if the warranty stipulates that all repair work must be done by this type of professional).
Ask your landlord for an alternative and temporary means of controlling the temperatures in your home
Depending on how badly broken the heating and cooling system is, and whether or not new parts need to be ordered for it, it might take a week or more for the HVAC contractor to fully repair it. If the repairs need to be done when the weather is unusually cold or hot, you must make sure that you ask your landlord for an alternative means of temporarily controlling your house's internal temperature.
If it's very hot, you might want to ask them for a few extra-large desk fans, as well as perhaps some black-out blinds that will stop the sun from getting into your house during the day and heating it up. If it's extremely cold, you might want to request portable heaters and extra blankets. Your landlord should comply with this request, as it is their responsibility to ensure that the property is safe for you to live in (this includes ensuring that the temperatures are neither dangerously low or high).