Live long and prosper.
Life exists and persists through a continuous orderly decay of energy states, and survival requires the continual discovery of new energy to pump into the system.
Heat death of the universe requires that the entire universe be essentially nothing but a bath of luke-warm photons.
More life means more energy consumption. The most energetic decays we know of occur in the creation of black-hole like entities of low mass, both in terms of emissions from the accretion disk and in terms of radiative Hawking evaporation, which (if actually physical) occurs at tremendous temperatures for low-mass black holes.
Matrioshka-layered energy converters around a micro-black hold core would also likely be the most powerful engines we can conceive of, so build lots of those, and go on trips around the universe. Send von Neumann machines around the universe to build more of everything, so that you can have warm coffee when you get to Andromeda after your (inertially-dampened) 400g accelerated journey there with ridiculous Delta-V expenditure.
In other words, we humans might very well simply continue doing whatever it is we're doing, just on a cosmic scale.