#1 if you know nothing about HVAC then you should stick with the cold weather (65°F is not cold weather) scenario.
#2 if you took NACHI training courses on HVAC, you should visually inspect the equipment, considering its age, type of equipment, is there a crankcase heater, is it a scroll compressor or a reciprocal, what has the temperature been like in the previous 48 hours, is the house occupied or vacant. If the equipment is not a total catastrophe (which requires replacement anyway), operate in the heating mode and increase the temperature within the building to provide a moderate heat load. Then turn on and verify that the compressor and fans operate. Turn it off.
#3 during the summer months if you really want to get fancy and become worthy of being called a “certified home inspector”, you can conduct a heating/cooling performance analysis with just your hand. The temperature receptors in your hand are actually more sensitive than the most expensive thermal imaging camera. You can very easily determine temperature differential by simply “laying hands on the equipment”.
Listen to the airflow entering the return register.
Put your hand in the airflow of the supply register.
Feel the suction refrigerant line at the outdoor unit or compressor.
Feel the liquid line leaving the outdoor condensing unit or at the metering device inside the unit (do not touch the discharge line of the compressor). Too hot to touch is a dirty condenser coil (even if it looks clean). If the outdoor ambient is below 95°F optimally you should not feel any significant temperature rise above your hand temperature (97°).
Put your hand in the airflow of the condenser (outdoor unit) fan, it should be not too hot and not too cool (normally a 30° temperature rise above ambient). Too hot is a dirty coil (even if it looks clean). Too cool has to do with refrigerant issues which you should have detected at the refrigerant lines.
If you have an electric or heat pump unit you can test the electric heaters by turning them on (emergency heat switch), and observing the increase in speed at the electric meter.
Heat pump in the heating mode: feel the suction refrigerant line (the big one), the warmer the outdoor air temperature, the hotter the line should feel (above 32°F ambient).
Observe any signs of oil leaks or staining. Listen for any unusual sounds or vibrations.
In five minutes, your done!
There obviously will be times when you cannot be comfortable with performing all of these procedures but at least you gave it a try.