If you had a planet with hostile conditions (25 atm pressure, 400° surface temp) would it be possible that a cave system could exist beneath the surface at a different temperature and pressure, or would the porousness of the crust equalize the two?
If the planet produces its own internal heat (like the Earth), any cave system that is below surface level will have a higher pressure and temperature than the surface (the difference might be minimal if the cave system is near the surface). If the planet doesn't produce its own internal heat (i.e. the core has cooled down to the point where it no longer produces any heat, and the mantle has had time to cool to the surface temperature and solidify), then only the pressure will go up with depth; the temperature will stay constant. (The inside of the planet will not cool down below the surface temperature as it can only lose heat by radiating it through the surface, and if the temperature of the inside is the same as the temperature at the surface, it has reached thermal equilibrium and will not cool further without the input of energy, e.g. via artificial cooling.)
The only way to have a lower pressure than the surface is either if the cave system is higher than the surface (e.g. a cave system at the top of Olympus Mons on Mars will have nearly zero atmospheric pressure, which is considerably lower than at the surface), or if the atmosphere in the the cave system is completely isolated from the surface; e.g. by some kind of sealed silo. (The reason for this is that the deeper you go, the greater the weight of air is above you, hence the greater the pressure is.)
How you implement this atmospheric seal is up to you; you could say that there is some natural huge glass chamber, solidified in the now-solid mantle, that completely encompasses the cave system you're interested in. Furthermore, there could be some kind of artificial cooling built into the glass chamber.
I'm not sure how this helps you in your story, but unless you go with magic, this is the way it'll work.
It can even have a different atmosphere like this cave in Romania. Basically, a waterproof layer has sealed-off the cave from the rest of the world for 5 million years. Chemosynthesis is prevalent among bacteria as light for photosynthesis is absent, so bacteria are primary producers. The atmosphere is poor in oxygen and poisonous. Temperature stays around 25c year-round. I assume if the cave remains intact while crust subduction occurs, temperatures may rise as well. There are much deeper caves which are already subject to high temperatures, and who knows what exotic life we may find there.