Tl/Dr: There are thermal limits if you get too much better than what we can see. They make it impossible to see better, even with the fanciest of equipment.
You may underestimate just how unbelievably pitch dark a cave is.
Fortunately, we can do math.
One of the first things a spelunker is taught to do in a cave is to turn out their light. You do this to learn just how dark a cave is. You do this to learn to appreciate why you need extra light sources. They're not optional.
Consider this structure in a cave. You have an opening 2 feet by 2 feet wide. Large enough to squeeze through. If you're a real spelunker, you won't even put the word "squeeze" there... its a huge opening! It leads into a room that is 10 feet wide, and there's another 2 foot by 2 foot opening on the other side. You'll find that roughly three thousandths of the light from your opening will reach the opening on the other side. Combine that with the reality that rocks absorb a lot of the light that hits them, and perhaps a thousandth of the light goes into the room beyond.
Outside, a nice sunlit space emits around 1000 cd/m^2. So one room in, you're lit by 1cd/m^2. It's roughly lit like a late sunset or sunrise.
Now go two rooms in. Now there's 1mcd/m^2. This is roughly moonlight in intensity.
Go three rooms in. Now there's 1ucd/m^2. At this point, we're at the absolute limits of human vision.
Now go four. 1ncd/m^2. Cats are going to have trouble seeing here.
If I may skip ahead a few rooms, at 7 rooms we run into a fascinating problem. Everything emits blackbody radiation do to thermal excitement. 7 rooms in, it turns out that the blackbody radiation from everything is comparable to the intensity of light that's made it through those 7 passages.
What does this mean? Not only is everything glowing evenly, but your own eyevalls are emitting this radiation too. You literally wont be able to see through your own lens because the lens will be glowing almost as bright as the scene itself.
So this says we have a very small region to work with. Rooms 5 and 6 are bright enough to avoid this blackbody issue, but too dark for a human eye to see. There's a mere order of 6 in brightness between those. That's the target for your darker sight.
Cats can see roughly 6x better than us. If I can handwave that up to 1 order of magnitude, that leaves 5 orders of magnitude of darksight which goes beyond what cats can see but stays above thermal limits.
You could probably get another order of magnitude via better processing. In such dark environments, you'd be moving slow. If you could get your eyes to slow down as well (avoiding saccades), you could probably increase your integration time (a.k.a. eyes on target time). That could probably give you another order of magnitude.
You could get another order of magnitude by dropping the resolution of your senses. When in dark environments like that, you really don't need good vision. Indeed, cats are known to have 20/100 vision or worse. Accepting even worse vision would permit you to capture more "photons per pixel," (though the human eye doesn't operate in pixels).
So that leaves you with 3 order of magnitude. 1,000 times darker than what you could see with cat eyes and long integration times is that thermal limit.
At that point, we're starting to turn to magic. Its rare for an organic body to push to within 3 orders of magnitude of such a fundamental limit. More likely it will evolve echolocation abilities, which will be much more effective in those settings. Indeed those who are practiced at echolocation can walk around perfectly without seeing anything at all. I've seen videos of blind people riding bikes, relying on nothing but sound to tell them where to go.