A manufacture coverts plastics into polymers via a PYROLYSIS $($Fired$-$Heater$/$Furnace$)$ process. The furnace generates $100,000k\frac{J}{s}$ of heat in which $80\%$ of the heat is used by the pyrolysis process and $20\%$ becomes a waste. An external cooling system contains cold water with volume flow$-$rate $(100\frac{m^3}{s})$ is added to the furnace to remove the waste heat. What is the resulting temperature increase to the cooling system?