In-Home Streaming
With a group of networked computers in a home, one high-performance PC/server acts as the brain for a set of "dumb" computers. Low-performance devices appear to run high-end applications (ex: video games) because they send the user's input to the high-performance device (PC/Server) and display its audio-video response.
You don't need a second gaming PC for your TV. You can just buy a cheap, quiet PC and use In-Home Streaming.