Streaming video is completely different from gaming relating to FPS.
Have no idea if Nvidia has full support for Linux. I would drop them line.
Overall system cooling for your application would be the question. Not so much the GPU cooling. GPU's will be in three configurations. Air cooled, Water cooled (self contained), Water cooled through open loop water system.
For your application I would not go with water cooling. What people fail to take into account is basically water cooling will do a general better job than "standard" air cooling. What happens if once a system heats up (eventually) water does not release heat as fast as an air cooled system. So they take a longer time to cool down. Running continuously I would look at a case that has a 200mm or 230mm main fan. These move more air at lower speeds and do a better overall job of system cooling.
Then I would look at a GPU with 2 or 3 fans. These will give a max cooling for the GPU, produce less noise as you can adjust them and the cooling is spread over more fans.
Also as far as the case look into one that besides having larger fans but has built in dust filters.
Remember valor, honor, independence, family & clan; I do whenever I hear the ceol mor, the "great music" of the Highland bagpipe. I swear upon the holy iron of my dirk that I will not forget.