You can keep a rotisserie chicken warm for 2 hours by wrapping the rotisserie chicken in some aluminum foil and placing it in the microwave without turning it on.
The aluminum foil will help to hold heat in and the small size of the microwave will help prevent too much heat from escaping.
You could also remove the rotisserie chicken from the plastic container wrap it in aluminum foil and place it in an oven pan and then occasionally turn the oven on on low heat such as 150 to 200 F to warm it every 20 to 30 minutes.
It is best to put a cold or room temperature rotisserie chicken in the refrigerator as putting a warm or hot rotisserie chicken in the refrigerator can lead to bacteria growing in the rotisserie chicken and other foods and make the refrigerator work harder to cool down.
You can leave rotisserie chicken out for 2 hours before refrigerating.
While the rotisserie chicken can be safe longer than a couple of hours at room temperature it is best to refrigerate the rotisserie chicken if not serving or eating it within 2 hours to prevent potential bacteria from growing on it.
It is safe to eat cooked chicken left out for 4 hours but best to refrigerate it before then.
While the health department has to regulate food establishments on when to throw out food and how long to leave out the food it does not mean that the food actually spoils or has bacteria after that time period.
Although it's not recommended to eat cooked chicken that is left out longer than 2 hours as it could potentially make you sick, it generally is okay to eat the cooked chicken that was left out longer than a couple of hours.
I've personally have eaten cooked chicken that was left out for 4 hours and even overnight before and never gotten sick from it.
Bacteria can grow rapidly on food left out at room temperature for more than 2 hours.
If food is left out in a room or outdoors where the temperature is 90 degrees F or hotter, food should be refrigerated or discarded within just 1 hour.
I don't make it a habit of eating cooked chicken or other meats or foods left out too long but when I've done so I was okay.
As long as the meat or cooked chicken still smells good or has no mold etc on it then it's generally safe to eat.
You could reheat it and kill off some bacteria that could be on the chicken.
The health department is not always right but they have to be so strict to prevent people from becoming sick and suing the food establishments and possibly leading to someone's death.
But at home it's just up to you and if it looks okay then it's usually okay to eat.
However if not eating the cooked chicken within an hour or so you should refrigerate it and it will keep for around 7 days.