Is it better to use an external display or stream to apple tv

I have a macbook pro 15 inch 2017 model and have had heating issues using an external display. After doing research, I found it has to do with the fact that the external display causes the computer's graphics card to overheat because it has to power both the computer and the external display. I was curious if using my apple tv to stream my computer instead of direct connecting to the external display would have any difference on performance and heating? Would it be better for my computer because the apple tv hardware would be loading graphics instead of the macbook or would the macbook still be loading everything and then streaming it to the tv?