I generally test the Gas Furnace’s all year long.
But, during this time of year it is sometimes not possible to get the home to cool down below 90 F during the typical 2 inspection time if the AC has been off. Most Thermostats will not activate the Heat above 90 degrees.
We are already getting 100 degrees days in my area. If the house is vacant, I turn the A/C on for a couple hours so the interior temp goes down enough for the thermostat activate the furnace.
Furnaces have a high-temp limit that will shut down if things get too hot.
No reason not to run furnaces because of ambient temps.
Heat pumps are not furnaces, so they do not apply.
Emergency Heat is for electric heat strips only.
Heat Pumps also have a high pressure limit (some require manual reset so you better know where to find it!) that will shut things down.
Not a good idea to stress anyone’s old unit for the sake doing more than you should be doing as a home inspector.
If your unit has a lock-out or an open limit switch, it would be plain stupid to by-pass them now wouldn’t it?