Warning to players - this answer is spoiler-y.
I just went through White Plume Mountain as a player. We had a party of four, and we nearly got TPKed several times.
Honestly, it's going to be difficult. You're going to want to be very clear when they are in a room where it is safe for them to have a short rest, because they're going to have to burn through those hit dice. I agree with the other reply that recommends having extra consumables around. Greater Healing Potions, Wands, scrolls. I'm assuming that your party members are capable of using the wands and scrolls - if not, you might want to give them some really nice magic items early on - but remember you're then stuck with those for your campaign unless you have a plan to get rid of them (maybe they're bound to the mountain, so once they leave the items vanish). I have been in campaigns where players were given strong items to get them through an overpowered set of encounters, only to have them wade through the next set. It can backfire.
There's a room with an apparent friend in the complex. Perhaps it is worth giving them a bookshelf that contains some strategic information on the dungeon, so that they can prepare. The BBEG might find that entertaining, so you should be able to justify it.
Remind your players that it's okay to run! We had a helm of teleportation, which of course didn't let us leave the Mountain, but did bounce us to the room mentioned above. We had two charmed, two with only a few hitpoints left at that point, so we ended up spending a while in that room until the charm wore off! (You may want to nerf Mr Charming - pretty sure you know who I'm talking about - it's a fun fight, but it's brutal)
Additional NPCs for players to run are also an option, with the caveats mentioned by @ant_aoe above. I recommend against running them yourself, as it will not be fun for the players if the DM has the majority of the action.