I've had my PI 3 running for 93 days without ever shutting down. Emulation Station goes into a dimmed mode after a few minutes. What that does for power consumption, I don't know.
4 hours since last play system temperature is 42c. We have 21c in house. I don't have a heat sink, but I haven't attached the top lid either.
The nice thing about having it running 24x7 is that is gets out of dimmed mode nicely by pushing the X-button on the Xbox 360 controller and you're good to go...