I don't think so. With hit dice, short rests and temp hit points you can do really well.
Hit dice provide at most one full heal-up without the aid of magic, short rests don't restore any HP on their own, and sources of THP that aren't magical in nature are pretty heavily limited. The only sources I'm aware of that can be given to other characters are Battle Master's Rally (usable at most 6 times per short rest, for at most 1d12+5 THP, at dramatic cost to fighting prowess) and the feats Inspiring Leader (which provides level+Cha mod THP once per short rest) and Chef (which provides proficieny bonus THP via a few "treats" after an hour's work).
Like, even if you had someone regularly pumping out the THP through these features, and actually get your DM and group on board for three short rests a day, you'd still only be getting
maybe the equivalent of one more full heal-up a day. At level (say) 9, relatively achievable for most groups, Inspiring Leader provides 14 THP (9+5) per short rest when even a Con 10 Wizard has 6+4×8=38 HP. Chef grants an extra +3d8 healing (one for each short rest) and a whopping
16 whole THP for an hour's work (in units of 4). And you'd be rolling 1d8+5 at best for Rally, giving 9.5 THP four times per short rest. Since none of these can stack, they must be carefully doled out so as to not waste them.
So at a level where even the most fragile characters (d6 HD, -1 Con mod) should have ~30 HP, you can get about 14+4+10 = 28 THP per short rest, if you manage them absolutely perfectly and never allow a single one to go to waste. The absolute most fragile character (5+3×8=29) gets, under ideal circumstances with no unfavorable rolls and no waste, about a full heal-up. A character like a Fighter or (God forbid) a high-Con Barbarian will get far less, relatively speaking. 15+10×8=95 HP, so 28 THP isn't even a third of a moderately high (16) Con Barbarian's HP, and even a Fighter or Paladin should have
at least 11+7×8=67 HP, getting less than half their HP as THP, again assuming perfect usage, zero waste.
I'm not as well-versed with 5e's damage numbers as I could be, but as I had understood it, growth of both damage output and HP values was the whole point of the so-called "bounded accuracy" idea?
For comparison, a 9th level Cleric doing something comparable to the BM, i.e. exclusively using spell slots to heal rather than anything more useful, generates 1d8 per slot level actual healing or 4+6+9+12=31, plus flat ability mod per spell cast, for a total of approximately 31×4.5+5×(4+3+3+3)=204.5 HP restored, not counting regained slots via burning Channel Divinity uses, nor any subclass features. They also have one daily 5th level slot, allowing 3d8+5=18.5 further healing applied to the whole group, which if we presume the usual minimum of 4 characters, that increases the Cleric's healing to 278.5 HP per day. For a similar party of four getting three short rests, each party member gets 28*3=84 THP, or about 336 THP. And all it took was a Fighter with maxed out Cha (at the expense of any other stat) blowing all of her damage bonus on THP, and someone else (or that fighter, if playing a race with a free starting feat). I will admit, I actually expected this to fall short of what magic can do and am slightly surprised that it does better. But I still am extremely skeptical that "THP and short rests" are anywhere near enough to actually deal with the expected damage output of 5e monsters.
Particularly given how often people expressly say that almost every fight should be "Deadly" because anything else is a cakewalk...
Oh, and don't forget: you only regain HALF your HD every long rest, not all of them. So if you're reliant on HD to keep going, better be okay with full-day breaks in between each adventuring day!