As entropy increases, the universe will evolve toward a thermodynamic equilibrium, and I understand that in a macroscopic sense, that is order since the temperature is the same everywhere. However, in a microscopic sense, it is chaotic, because as you increase temperature the movement of the atoms get faster and faster, now what I am unable to understand is, why is the heat death scenario considered a disorder? If it means the universe will be getting really cold, doesn't the mean that in the microscopic level the atoms will be moving very slowly? Isn't that more of an order than a disorder?
Remember that the universe will have expanded to an extremely large size by then. The expansion results in both the cooldown (as the matter/energy density gets diluted) and the increase in entropy (as the energy's positional spread increases). The increase in the positional contribution to the entropy dominates the decrease in the momentum contribution.
I doubt the "heat death" very seriously. First, our Universe is not enclosed system. We cannot ensure somehow that "thermodynamic closeness" could be verified. Even if we assume that, we do not know exact parameters of Universe to verify cosmology assumptions about the evolution of Universe, i.e. intensity of turning stars into black holes, gravitational evolution of Universe etc.
Also, we do not know if so called "global warming" exists ("does not" is not ruled out too), which is the problem of lesser scale, which could be solved simply by building science all over the world. Yet, there is infinitely small number of scientists to even rule out that one "small problem".