I have a Champion (Household 2000+) and have been making mostly my favorite apple/carrot juice with it. I always get moist pulp and usually there's some stuck in the juicer including right behind the screen. I thought this was unacceptable as pulp-ejecting juicers should be able to be used all day without washing. I tried to solve this by running the pulp through it again and again. But eventually I ended up setting up a juice press myself and started to use Champion as a grinder. (You can read my postings regarding this below under "Juice Press or Greenstar.")
Anyway when I tried celery, its fiber got all around the blades and never came out. I've never run sweet potatoes through it but done beets and I thought it was okay except for beet greens.
When you get warm juice and pulp, I believe this means your motor is heating up because you're feeding veggies too fast. So you may want to slow down and at the same time set your fridge's temperature low to keep vegetables cold (so that you can keep enzymes alive when you juice it.)