I usually add some cold water, and then it is OK to use. The plastic can melt and deform at 225F so boiling hot water sitting in the trap is not a great idea long term, so adding a small amount of water will cool it below 150F quickly!
We try hard to not put any food down the drain. In the Florida heat, the gray tank can get really foul smelling. We wipe out all of our plates, pans, etc with newspapers or paper towels before washing them. Pasta water would get thrown into the bushes after rinsing any other dirty pans or dishes with it first. Hot water wouldn't hurt the drains or tanks.
I won't for two reasons - the hot water can affect the seals in the drain and I'm not taking chances with my moving condo. Second - something too gooey, in my opinion, to put down into the holding tank. I let it cool, then either put part down the black tank, if we're not boondocking, or put the entire thing into the fire pit to put it out. On one occasion I cooked rice pasta and the water was thick like gelatin when it cooled, so I put it in double zip loc bags and put it in the trash.
2011 Bighorn 3055RL
2011 F350 SD CC DRW 6.7L Diesel Lariat, Hensley BD3 with Ford Under-Bed Adaptor
Dave & Renee plus (Champ, Molly, and Paris in spirit), Missy, Maggie, and now Mica!