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Other questions concern what to do to prevent or live through or slow the eventual heat death of the universe. This civilization is different: they want to bring it on, and they can't wait!
This has consumed their culture and led to their increased mastery of physics and evolution to a Type II (and still growing) civilization.
What kind of things do they do as part of this goal?
Do More Stuff
Since the entropy of a system can never decreased, and as energy is transformed, it become increasingly harder to utilize, all they need to do is use as much energy as possible as quickly as possible, hastening their inevitable demise, along with everyone else with them (and for that same reason, they may end up making a LOT of enemies).
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.
I assume you're talking about a Kardashev level 4 civilization or higher. It could convert every planet, star, and white dwarf in reach into black holes. Black holes maximize entropy, constrain all the available mass/energy in their reach, and would convert all that mass and energy into gravitational waves.
After that, nothing in the universe would be usable.
Push matter together into black holes. Use a giant broom to push stars at the edges of the galaxies towards the centres.
