When to determine if your central heating and air conditioning system breakdown is an actual HVAC emergency or not depends on a few factors.
The first being do you have any portable HVAC equipment in the house? If you have a portable space heater and it is winter or you have a portable air conditioning system and it is the dead heat of summer, then you do not have a heating and cooling emergency on your hands.
You can use your portable space heater or portable air conditioning system to keep you warm or cool while you wait for a heating and air conditioning specialist from the local heat and a/c company to come out and repair your central heating and air conditioning system unit. However if you do not have a portable space heater or a portable air conditioning system then you have a true HVAC emergency on your hands! You would be best suited to call for emergency HVAC services from your local heat and a/c company and pay the extra money to have them come out right away. If they can not or do not offer emergency heating and air conditioning home services, then you would go to a hotel until they could arrive at your home to fix your central heat and a/c unit. That is the general basics on what is a heating and cooling emergency and what is not. Use it however you would like, but these are the facts. Plain and simple.