Hmm, adding a second screen (the TV) to the side off the first and moving the steam window there is not what you want?
I guess you could try those methods of running a second X server and direct its output to the TV? Never did that myself though. The laptop bumblebee stuff could be an convenient way to set that up, as it is doing that in the background.

Thanks for your answer Julius.

I tried to setup nvidia-setings with 2 separate X screens (monitor and TV) and launched Steam Big Picture on the TV (console like). That worked until I tried to launch a game and it appeared on my monitor instead of TV.
¿Is there a way to make Steam open games his same screen by default?

I know that another option is set my TV as the primary display, but it'll screw my working desktop.

P.S: I liked the idea of running a second X server and direct its output to the TV, but I only have 1 GPU (my CPU is rather old).

- EDIT -

Just found a solution, in my system:
xrandr --output HDMI-0 --primary;steam -bigpicture;xrandr --output DVI-I-0 --primary

That way when I start Steam it changes the primary screen to my TV and as soon as I close it, it revert back to my monitor again.

Hope this helps!