I have to agree with the previous posters. The Note 8 compared to the Note 7, S7 Edge and S7 has vertually none of the heating issues that the 7 series did.
Heavy use with and without charger plugged in, barely warm.
As the previous posters, I can attest the 7 series phones got hot, very hot after heavy usage. I saw a YouTube video of the Note 8 being torn down yesterday and saw there is a heat pipe from the processor that is designed to channel the heat from the CPU to the phone's frame. Next gen CPU must really run cooler.