Basically, the title. Trying to figure out how reasonable stealth in space would function, and while I have mitigated it, I am looking for methods to improve it. But mainly, is creating a sort of heat sink structure with a sufficient number of entangled particles viable to transfer enough heat to keep a crew-less ship near enough to or at background temperature?
Particle entanglement has no bearing in hiding heat emissions.
If you want to emit energy with a low probability of detection, use particles that interact very weakly with the normal matter/fields.
I don't know, eject that energy as neutrinos or "highly energetic beams of dark matter".
Of course, the current level of science and the reality as we know it don't allow you to use such means, so you'll have to handwave them.
However, it is very unlikely that you could convert heat into high energy neutrino beams - if they interact so weakly with the matter/fields that there are good chances to stay undetected, it will also interact so weakly with the matter/fields that you won't be able to confine or accelerate them.
So you'll have to handwave vigorously enough to use them (but not strong enough to generate more heat than you can exhaust).
Entangled particles share quantum states (stuff they do at the subatomic scale), but have different kinetic properties (how they move through space). Heat is a form of kinetic energy; so, cooling one half of the quantum pair should have no effect on the other half's temperature.
Another theoretical phenomenon similar to quantum entanglement might work for you though. Wormholes, like quantum entanglement, do freaky stuff at a distance. But instead of shared quantum states, wormholes create shortcuts through timespace that make two faraway places simultaneously adjacent. By connecting a wormhole to a far away cooling apparatus, you could pump cooling fluids between these distant points as though they were physically connected.
Just bare in mind that some theories regarding wormholes say it is impossible to move them or that they can not be created ad-hoc to where you want them to come out; so, you'd need to account for this as well. Best solution I can think of is that your ship has to stop, then it punches a wormhole to whatever random place in the galaxy it can find, then lowers its heat exchanger into the wormhole which may come out just some random place lightyears away.
hmm, lets see. No or at least not how you think. There is an easier way though: just turn everything off because of the law of conservation of momentum you could just use liquid nitrogen to cool it down and then vent the gas and even with your engines off you wont stop. if you don't want to alert anyone just use heat sinks to radiate off heat. only keeping basic functions on can help it stay cool. no fanciness required, but you would need to spin so it is heated evenly. the cryogen fluid i suggested does seem like the coolest one tho. i'm no expert at entangled particles but i'm pretty sure they dont act how you think they do.