Where does the heat go NOW? It's a closed system (as far as we know).
Heat is energy, and it's either going into matter or more energy. So it becomes more Complex.
However, we have more Space -- so it's better to say that "heat has diffused, or become a more complex interaction." For instance, if all force at one time went in one direction, it "seems" like there is less energy if there is equal and opposing force. Also, is all particles in a system are headed in one direction - they still have force, but the energy seems to "be at rest" relative to that system. At least if we keep things in a Newtonian Universe.
I think however, that much of the energy has "sublimated" -- or is at a frequency we don't interact with. Like what is called quantum fluctuations or "vacuum energy". The "cold matter" we interact with, has a much lower frequency and so rides on top of a lot of the energy (like a carrier wave) that existed from the Big Bang. Not sure if that is accepted theory, but it's the obvious answer that springs to mind if I'm sticking with a General Relativity Universe.
To think about it is kind of awesome; right now, there is as much energy and activity as when the Universe first "exploded" into existence -- however, I theorize we have a 12 dimensional Universe, so a lot of the energy is being traded to a subset of 4 dimensions while we "appear" to have more empty space. The side effect of this interaction produces what we call gravity. However, that's just my theory, but it seems more simple than the other models. ;-)