Do you remove the Feeder cap from Food Processor when you're gonna puree a hot item ?

Well I don't know what kind of food processor you have. I have a Kitchen Aid. I always remove the feeder cap unless I'm using it as a plunger so I don't have to clean it.

But if leaving the cap on seals your food processor, pull it. If it doesn't seal the food processor I wouldn't worry about it.

Additionally, are you sure that processing something hot off the stove won't crack the bowl of your food processor?

This is a recipe for minor disaster. As a professional catering and restaurant chef i've seen it turned into a major one, walls and ceilings coated with black beans or broccoli, cooks on their way to ER. Play it safe and let the food cool a little. If you're using a blender DO NOT clamp down the top, you've got to let air get in there. If you're using a processor set up like a Cuisinart, take the plunger out, and lay a towel over the feed tube. This is also a really good time to learn the benefits of an old school hand cranked food mill. These classic tools allow you to control the coarse-fine/ness of the soup or puree, and do a much better job on foods like mashed potatoes. They're also cheap and almost indestructible, and give you a nice little upper body workout to boot! Try one!

You want it closed up, but not SEALED, use the lid of the food processor bowl as a shield from hot liquefying food. It won't be enough to prevent the steam from escaping. This is enough compromise to allow for safety. You don't want to redecorate your kitchen or your face with hot pureed food, even if it means you have to stop the machine, dismantle the bowl, and add more.

The only reason to leave it open is if you are feeding it something, such as adding carrots or cabbage for a coleslaw and collecting it in the bottom, or adding oil to a salad dressing as it blends so it emulsifies. Otherwise, closed up means that the food processor manufacturer doesn't get sued when some heehaw cuts his hand off.