You are correct, time cannot possibly reverse or we would not be here. Reversal of time would allow heat to move from cooler areas to hotter areas. The end result is all heat in the universe would end up at the same spot. Sounds like a Big Bang situation to me.
Going back to the wilderness frontier, the perfect but energy-less lawns going back to wild forest high energy weeds, the greater order of things so many thinks is the ultimate in disorder, is what the universes and life always do. What entropy is, including the collapse of complexity, and where it tends, the Planck heat and energy constant -- among others -- Horizon. Several times I've doubled it as the Big Bang Horizon and more, though, in fact, it is the collapsed cosmological constant (/\) of the Planck Horizon. I get tired of 'El Ponderosa'. I'm correct in the way of always going "back to the future."
The constant of the Planck Horizon; The constant turnaround to the Planck Horizon, the relentless and inevitable return in heat and energy to the primal Horizon of all the discreet quanta spheres macro and micro, is the nature of things. The universe doesn't lose or dissipate, or gain, things, not anything, including its heat and energy.
Refer to #237 in this thread.
An endless infinity of 0-point centers to universes have an endless infinity of collapsed horizons "at a distance" creating an infinity of horizon universes (fractal zooms universe structure). An infinity of "infinite potentials" in expanding universes infinitely fulfilled (those asymptotic straight lines of expansionism never do meet curvature). And, to borrow slightly from J. R. R. Tolkien, one Horizon (the Planck Horizon) to rule them all.
So, in effect, you are right, the end result is all heat in the universe ends up at the same spot, the same longitudinal point in the end. a constant Big Little Bang, or Little Big Bang, situation. An eternal fire is more like it. Since heat and energy relentlessly radiate from that Horizon as well as relentlessly, inevitably, tending back to it (in and as "entropy").
The Infinite MULTIVERSE (infinitely multi-dimensional) Universe. Same base throughout though. As Stephen Hawking said, the dice "they're loaded!"