It always wise to let the generator engine to warm up for a minute or two before putting a load on it. Trying to start with a load may not work and/or may be detrimental to its longevity.
After a big load it is also a good idea to let it idle a few minutes to cool. Always have the load off when shutting down.
If you are exercising your generator I would assume it has not been run for awhile. Based on that, a quick check of the oil level is also a good idea.
It is also an opportunity to check the air filter, look for oil leaks, fuel leaks, anything out of the ordinary. Best to catch any of that before you start it and before you leave for a nice trip,
I keep a log on the air filter, oil changes and fuel filter changes. A good idea for any engine.
2017 SLX 195RB
2014 Jeep Grand Cherokee Overland, gas 3.7 V6
Andersen WDH hitch
Dometic Milenco Aero mirrors