If you dumped waste heat directionally it would act as a photon rocket.

If you somehow reflected all the light of a star in one direction, the momentum change in the light would produce thrust on the reflector (much less than is needed to move a star), and since no substance is 100% reflective the huge amount of surface area would nonetheless heat up and be visible in the infrared due to its vast surface area. The same is true of any substance directing waste thermal radiation - you can shunt most of it in some direction the material will definitely reach an equilibrium temperature warmer than the cosmic microwave background anyway.

Furthermore, all the energy would eventually get absorbed/used SOMEWHERE and become heat. Local conversion of energy to other forms would also always involve waste heat production.

As far as I am aware, black hole surface gravity is analogous to temperature and surface area is analogous to entropy when you start digging into their thermodynamics. Dumping waste thermal radiation in will make them bigger and they will eventually re-radiate thermal radiation via the Hawking mechanism in the far future.