Question

​At heat death the universe _____.

​A) reaches thermal equilibrium B) cools down C) heats up

Answer 1

We know that if there is difference of tempreture, then heat flows from hight tempreture to low tempreture. Using this property of heat, engines do mechanical work done. But if the universe reached at work thermal equlibrium, i.e. attains same tempreture everywhere, then there is no more heat flow. And thus all the thermodynamic process stops there. This end is known as thermal/heat death of universe.

Let us consider an example. Let's consider an electric bulb. In it, electrical energy converts into light and heat energy. But then, this heat will become unavailable and remains as unavailable energy of universe. Those unavailable energy increases the entropy of universe.
Now if you carefully look in any process, you can see that finally heat energy will generated and remains as unavailable energy of universe. Thus entropy of universe is always increasing (2nd law of thermodynamics). This unavailable energy leads to the thermal equilibrium of universe and which leads to heat death of universe.

So, heat death of universe is -- (A) reaches at thermal equilibrium (Ans)

(From our previous discussion, it is clear that other two options ( B & C) are wrong.