The universe is becoming more and more diverse. The initial probes would be rather non-relativistic, but as they spread they can become faster. While the probes spread outward, building a network of civilisation behind them, the oldest parts around the core begins to suffer an energy shortage. The time at this happens depends on how fast the civilisation is using up available energy, but sooner or later it is going to run out. The stars have died long ago, and civilisation have used up most available energy.
Energy is at a premium, and matter is gradually converted to meet the remaining demands.
As the universe begins to collapse, the civilisation begins to exploit the anisotropy of the universe. By moving around matter on immense scales the collapse can be made more anisotropic, and the shear energy exploited. The cosmic background radiation will slowly grow stronger, but not as fast in all directions. This could be used to drive a heat pump, but most probably the posthuman beings of this era have devised more elegant solutions. As the collapse speeds up, the amount of available energy grows more and more, and life returns everywhere.